Results of Bessel Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 10.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}+(z^{2}-\nu^{2})w = 0} | (z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)+((z)^(2)- (nu)^(2))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ z*D[w, z]+((z)^(2)- \[Nu]^(2))* w == 0 |
Failure | Failure | Failed [217 / 300] 217/300]: [[-.8660254040e-9-2.000000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}-.8660254040e-9-2.000000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)} |
Failed [240 / 300]
{Complex[1.1102230246251565*^-16, 2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[1.1102230246251565*^-16, 2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
| 10.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}} | BesselJ(nu, z) = ((1)/(2)*z)^(nu)* sum((- 1)^(k)*(((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity) |
BesselJ[\[Nu], z] == (Divide[1,2]*z)^\[Nu]* Sum[(- 1)^(k)*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{\BesselJ{\nu}@{z}\cos@{\nu\pi}-\BesselJ{-\nu}@{z}}{\sin@{\nu\pi}}} | BesselY(nu, z) = (BesselJ(nu, z)*cos(nu*Pi)- BesselJ(- nu, z))/(sin(nu*Pi)) |
BesselY[\[Nu], z] == Divide[BesselJ[\[Nu], z]*Cos[\[Nu]*Pi]- BesselJ[- \[Nu], z],Sin[\[Nu]*Pi]] |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-n}@{z} = (-1)^{n}\BesselJ{n}@{z}} | BesselJ(- n, z) = (- 1)^(n)* BesselJ(n, z) |
BesselJ[- n, z] == (- 1)^(n)* BesselJ[n, z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{-n}@{z} = (-1)^{n}\BesselY{n}@{z}} | BesselY(- n, z) = (- 1)^(n)* BesselY(n, z) |
BesselY[- n, z] == (- 1)^(n)* BesselY[n, z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.4#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{-n}@{z} = (-1)^{n}\HankelH{1}{n}@{z}} | HankelH1(- n, z) = (- 1)^(n)* HankelH1(n, z) |
HankelH1[- n, z] == (- 1)^(n)* HankelH1[n, z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.4#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{-n}@{z} = (-1)^{n}\HankelH{2}{n}@{z}} | HankelH2(- n, z) = (- 1)^(n)* HankelH2(n, z) |
HankelH2[- n, z] == (- 1)^(n)* HankelH2[n, z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.4#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \BesselJ{\nu}@{z}+i\BesselY{\nu}@{z}} | HankelH1(nu, z) = BesselJ(nu, z)+ I*BesselY(nu, z) |
HankelH1[\[Nu], z] == BesselJ[\[Nu], z]+ I*BesselY[\[Nu], z] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.4#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \BesselJ{\nu}@{z}-i\BesselY{\nu}@{z}} | HankelH2(nu, z) = BesselJ(nu, z)- I*BesselY(nu, z) |
HankelH2[\[Nu], z] == BesselJ[\[Nu], z]- I*BesselY[\[Nu], z] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.4#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2}\left(\HankelH{1}{\nu}@{z}+\HankelH{2}{\nu}@{z}\right)} | BesselJ(nu, z) = (1)/(2)*(HankelH1(nu, z)+ HankelH2(nu, z)) |
BesselJ[\[Nu], z] == Divide[1,2]*(HankelH1[\[Nu], z]+ HankelH2[\[Nu], z]) |
Successful | Successful | - | Successful [Tested: 70] |
| 10.4#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{1}{2i}\left(\HankelH{1}{\nu}@{z}-\HankelH{2}{\nu}@{z}\right)} | BesselY(nu, z) = (1)/(2*I)*(HankelH1(nu, z)- HankelH2(nu, z)) |
BesselY[\[Nu], z] == Divide[1,2*I]*(HankelH1[\[Nu], z]- HankelH2[\[Nu], z]) |
Successful | Successful | - | Successful [Tested: 70] |
| 10.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-\BesselY{\nu}@{z}\cos@{\nu\pi}\right)} | BesselJ(nu, z) = csc(nu*Pi)*(BesselY(- nu, z)- BesselY(nu, z)*cos(nu*Pi)) |
BesselJ[\[Nu], z] == Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- BesselY[\[Nu], z]*Cos[\[Nu]*Pi]) |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.4#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{-\nu}@{z} = e^{\nu\pi i}\HankelH{1}{\nu}@{z}} | HankelH1(- nu, z) = exp(nu*Pi*I)*HankelH1(nu, z) |
HankelH1[- \[Nu], z] == Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z] |
Successful | Failure | - | Successful [Tested: 70] |
| 10.4#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{-\nu}@{z} = e^{-\nu\pi i}\HankelH{2}{\nu}@{z}} | HankelH2(- nu, z) = exp(- nu*Pi*I)*HankelH2(nu, z) |
HankelH2[- \[Nu], z] == Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z] |
Successful | Failure | - | Successful [Tested: 70] |
| 10.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = i\csc@{\nu\pi}\left(e^{-\nu\pi i}\BesselJ{\nu}@{z}-\BesselJ{-\nu}@{z}\right)} | HankelH1(nu, z) = I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z)) |
HankelH1[\[Nu], z] == I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z]) |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\csc@{\nu\pi}\left(e^{-\nu\pi i}\BesselJ{\nu}@{z}-\BesselJ{-\nu}@{z}\right) = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-e^{-\nu\pi i}\BesselY{\nu}@{z}\right)} | I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z)) = csc(nu*Pi)*(BesselY(- nu, z)- exp(- nu*Pi*I)*BesselY(nu, z)) |
I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z]) == Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[- \[Nu]*Pi*I]*BesselY[\[Nu], z]) |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = i\csc@{\nu\pi}\left(\BesselJ{-\nu}@{z}-e^{\nu\pi i}\BesselJ{\nu}@{z}\right)} | HankelH2(nu, z) = I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z)) |
HankelH2[\[Nu], z] == I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z]) |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\csc@{\nu\pi}\left(\BesselJ{-\nu}@{z}-e^{\nu\pi i}\BesselJ{\nu}@{z}\right) = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-e^{\nu\pi i}\BesselY{\nu}@{z}\right)} | I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z)) = csc(nu*Pi)*(BesselY(- nu, z)- exp(nu*Pi*I)*BesselY(nu, z)) |
I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z]) == Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselY[\[Nu], z]) |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\BesselJ{-\nu}@{z}} = \BesselJ{\nu+1}@{z}\BesselJ{-\nu}@{z}+\BesselJ{\nu}@{z}\BesselJ{-\nu-1}@{z}} | (BesselJ(nu, z))*diff(BesselJ(- nu, z), z)-diff(BesselJ(nu, z), z)*(BesselJ(- nu, z)) = BesselJ(nu + 1, z)*BesselJ(- nu, z)+ BesselJ(nu, z)*BesselJ(- nu - 1, z) |
Wronskian[{BesselJ[\[Nu], z], BesselJ[- \[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\BesselJ{-\nu}@{z}+\BesselJ{\nu}@{z}\BesselJ{-\nu-1}@{z} = -2\sin@{\nu\pi}/(\pi z)} | BesselJ(nu + 1, z)*BesselJ(- nu, z)+ BesselJ(nu, z)*BesselJ(- nu - 1, z) = - 2*sin(nu*Pi)/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z] == - 2*Sin[\[Nu]*Pi]/(Pi*z) |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\BesselY{\nu}@{z}} = \BesselJ{\nu+1}@{z}\BesselY{\nu}@{z}-\BesselJ{\nu}@{z}\BesselY{\nu+1}@{z}} | (BesselJ(nu, z))*diff(BesselY(nu, z), z)-diff(BesselJ(nu, z), z)*(BesselY(nu, z)) = BesselJ(nu + 1, z)*BesselY(nu, z)- BesselJ(nu, z)*BesselY(nu + 1, z) |
Wronskian[{BesselJ[\[Nu], z], BesselY[\[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]*BesselY[\[Nu], z]- BesselJ[\[Nu], z]*BesselY[\[Nu]+ 1, z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\BesselY{\nu}@{z}-\BesselJ{\nu}@{z}\BesselY{\nu+1}@{z} = 2/(\pi z)} | BesselJ(nu + 1, z)*BesselY(nu, z)- BesselJ(nu, z)*BesselY(nu + 1, z) = 2/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*BesselY[\[Nu], z]- BesselJ[\[Nu], z]*BesselY[\[Nu]+ 1, z] == 2/(Pi*z) |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\HankelH{1}{\nu}@{z}} = \BesselJ{\nu+1}@{z}\HankelH{1}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{1}{\nu+1}@{z}} | (BesselJ(nu, z))*diff(HankelH1(nu, z), z)-diff(BesselJ(nu, z), z)*(HankelH1(nu, z)) = BesselJ(nu + 1, z)*HankelH1(nu, z)- BesselJ(nu, z)*HankelH1(nu + 1, z) |
Wronskian[{BesselJ[\[Nu], z], HankelH1[\[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]*HankelH1[\[Nu], z]- BesselJ[\[Nu], z]*HankelH1[\[Nu]+ 1, z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\HankelH{1}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{1}{\nu+1}@{z} = 2i/(\pi z)} | BesselJ(nu + 1, z)*HankelH1(nu, z)- BesselJ(nu, z)*HankelH1(nu + 1, z) = 2*I/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*HankelH1[\[Nu], z]- BesselJ[\[Nu], z]*HankelH1[\[Nu]+ 1, z] == 2*I/(Pi*z) |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\HankelH{2}{\nu}@{z}} = \BesselJ{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{2}{\nu+1}@{z}} | (BesselJ(nu, z))*diff(HankelH2(nu, z), z)-diff(BesselJ(nu, z), z)*(HankelH2(nu, z)) = BesselJ(nu + 1, z)*HankelH2(nu, z)- BesselJ(nu, z)*HankelH2(nu + 1, z) |
Wronskian[{BesselJ[\[Nu], z], HankelH2[\[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- BesselJ[\[Nu], z]*HankelH2[\[Nu]+ 1, z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{2}{\nu+1}@{z} = -2i/(\pi z)} | BesselJ(nu + 1, z)*HankelH2(nu, z)- BesselJ(nu, z)*HankelH2(nu + 1, z) = - 2*I/(Pi*z) |
BesselJ[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- BesselJ[\[Nu], z]*HankelH2[\[Nu]+ 1, z] == - 2*I/(Pi*z) |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\HankelH{1}{\nu}@{z},\HankelH{2}{\nu}@{z}} = \HankelH{1}{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\HankelH{1}{\nu}@{z}\HankelH{2}{\nu+1}@{z}} | (HankelH1(nu, z))*diff(HankelH2(nu, z), z)-diff(HankelH1(nu, z), z)*(HankelH2(nu, z)) = HankelH1(nu + 1, z)*HankelH2(nu, z)- HankelH1(nu, z)*HankelH2(nu + 1, z) |
Wronskian[{HankelH1[\[Nu], z], HankelH2[\[Nu], z]}, z] == HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\HankelH{1}{\nu}@{z}\HankelH{2}{\nu+1}@{z} = -4i/(\pi z)} | HankelH1(nu + 1, z)*HankelH2(nu, z)- HankelH1(nu, z)*HankelH2(nu + 1, z) = - 4*I/(Pi*z) |
HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z] == - 4*I/(Pi*z) |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.6#E3X | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselJ{0}'@{z} = -\BesselJ{1}@{z}} | diff( BesselJ(0, z), z$(1) ) = - BesselJ(1, z) |
D[BesselJ[0, z], {z, 1}] == - BesselJ[1, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#E3X | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselY{0}'@{z} = -\BesselY{1}@{z}} | diff( BesselY(0, z), z$(1) ) = - BesselY(1, z) |
D[BesselY[0, z], {z, 1}] == - BesselY[1, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#E3Xa | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{1}{0}'@{z} = -\HankelH{1}{1}@{z}} | diff( HankelH1(0, z), z$(1) ) = - HankelH1(1, z) |
D[HankelH1[0, z], {z, 1}] == - HankelH1[1, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#E3Xa | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{2}{0}'@{z} = -\HankelH{2}{1}@{z}} | diff( HankelH2(0, z), z$(1) ) = - HankelH2(1, z) |
D[HankelH2[0, z], {z, 1}] == - HankelH2[1, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{\nu-1}(z)+f_{\nu+1}(z) = (2\nu/\lambda)z^{-q}f_{\nu}(z)} | f[nu - 1]*(z)+ f[nu + 1]*(z) = (2*nu/ lambda)* (z)^(- q)* f[nu]*(z) |
Subscript[f, \[Nu]- 1]*(z)+ Subscript[f, \[Nu]+ 1]*(z) == (2*\[Nu]/ \[Lambda])* (z)^(- q)* Subscript[f, \[Nu]]*(z) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu+1}-p_{\nu-1} = -\frac{2\nu}{a}q_{\nu}-\frac{2\nu}{b}r_{\nu}} | p[nu + 1]- p[nu - 1] = -(2*nu)/(a)*q[nu]-(2*nu)/(b)*r[nu] |
Subscript[p, \[Nu]+ 1]- Subscript[p, \[Nu]- 1] == -Divide[2*\[Nu],a]*Subscript[q, \[Nu]]-Divide[2*\[Nu],b]*Subscript[r, \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{\nu+1}+r_{\nu} = \frac{\nu}{a}p_{\nu}-\frac{\nu+1}{b}p_{\nu+1}} | q[nu + 1]+ r[nu] = (nu)/(a)*p[nu]-(nu + 1)/(b)*p[nu + 1] |
Subscript[q, \[Nu]+ 1]+ Subscript[r, \[Nu]] == Divide[\[Nu],a]*Subscript[p, \[Nu]]-Divide[\[Nu]+ 1,b]*Subscript[p, \[Nu]+ 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{\nu+1}+q_{\nu} = \frac{\nu}{b}p_{\nu}-\frac{\nu+1}{a}p_{\nu+1}} | r[nu + 1]+ q[nu] = (nu)/(b)*p[nu]-(nu + 1)/(a)*p[nu + 1] |
Subscript[r, \[Nu]+ 1]+ Subscript[q, \[Nu]] == Divide[\[Nu],b]*Subscript[p, \[Nu]]-Divide[\[Nu]+ 1,a]*Subscript[p, \[Nu]+ 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{\nu} = \tfrac{1}{2}p_{\nu+1}+\tfrac{1}{2}p_{\nu-1}-\frac{\nu^{2}}{ab}p_{\nu}} | s[nu] = (1)/(2)*p[nu + 1]+(1)/(2)*p[nu - 1]-((nu)^(2))/(a*b)*p[nu] |
Subscript[s, \[Nu]] == Divide[1,2]*Subscript[p, \[Nu]+ 1]+Divide[1,2]*Subscript[p, \[Nu]- 1]-Divide[\[Nu]^(2),a*b]*Subscript[p, \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu}s_{\nu}-q_{\nu}r_{\nu} = 4/(\pi^{2}ab)} | p[nu]*s[nu]- q[nu]*r[nu] = 4/((Pi)^(2)* a*b) |
Subscript[p, \[Nu]]*Subscript[s, \[Nu]]- Subscript[q, \[Nu]]*Subscript[r, \[Nu]] == 4/((Pi)^(2)* a*b) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{z} = -\frac{(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+\frac{2}{\pi}\ln@{\tfrac{1}{2}z}\BesselJ{n}@{z}-\frac{(\tfrac{1}{2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(\digamma@{k+1}+\digamma@{n+k+1})\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}} | BesselY(n, z) = -(((1)/(2)*z)^(- n))/(Pi)*sum((factorial(n - k - 1))/(factorial(k))*((1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(2)/(Pi)*ln((1)/(2)*z)*BesselJ(n, z)-(((1)/(2)*z)^(n))/(Pi)*sum((Psi(k + 1)+ Psi(n + k + 1))*((-(1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity) |
BesselY[n, z] == -Divide[(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(n - k - 1)!,(k)!]*(Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]*Log[Divide[1,2]*z]*BesselJ[n, z]-Divide[(Divide[1,2]*z)^(n),Pi]*Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(-Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [6 / 21]
{Plus[-0.4244131815783875, Times[0.4244131815783876, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[32, 3], Power[1.5, -6], Plus[3, Times[Rational[1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]}Plus[-0.8841941282883073, Times[0.3183098861837907, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[32, 3], Power[1.5, -6], Plus[3, Times[Rational[1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][2.0]]], {Rule[n, 2], Rule[z, 1.5]} |
| 10.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\dotsi\right)} | BesselY(0, z) = (2)/(Pi)*(ln((1)/(2)*z)+ gamma)* BesselJ(0, z)+(2)/(Pi)*(((1)/(4)*(z)^(2))/((factorial(1))^(2))-(1 +(1)/(2))*(((1)/(4)*(z)^(2))^(2))/((factorial(2))^(2))+(1 +(1)/(2)+(1)/(3))*(((1)/(4)*(z)^(2))^(3))/((factorial(3))^(2))- .. ) |
BesselY[0, z] == Divide[2,Pi]*(Log[Divide[1,2]*z]+ EulerGamma)* BesselJ[0, z]+Divide[2,Pi]*(Divide[Divide[1,4]*(z)^(2),((1)!)^(2)]-(1 +Divide[1,2])*Divide[(Divide[1,4]*(z)^(2))^(2),((2)!)^(2)]+(1 +Divide[1,2]+Divide[1,3])*Divide[(Divide[1,4]*(z)^(2))^(3),((3)!)^(2)]- \[Ellipsis]) |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[0.08653583575184755, 0.12491815695491987], Times[-0.6366197723675814, Plus[Complex[0.13592303240740744, 0.19620888054491187], Times[-1.0, …]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.07160606681826986, -0.15074612001799426], Times[-0.6366197723675814, Plus[Complex[-0.11248553240740736, -0.23680382134730746], Times[-1.0, …]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\mu}@{z} = (\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}\EulerGamma@{\mu+k+1}}} | BesselJ(nu, z)*BesselJ(mu, z) = ((1)/(2)*z)^(nu + mu)* sum((nu + mu + k + 1[k]*(-(1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)*GAMMA(mu + k + 1)), k = 0..infinity) |
BesselJ[\[Nu], z]*BesselJ[\[Mu], z] == (Divide[1,2]*z)^(\[Nu]+ \[Mu])* Sum[Divide[Subscript[\[Nu]+ \[Mu]+ k + 1, k]*(-Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]*Gamma[\[Mu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [300 / 300]
{Plus[Complex[0.18482793500467376, -0.06270111308873656], Times[Complex[-0.17426361621858172, -0.037827155645948574], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -2], Subscript[Plus[1, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], k]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.47215054540190965, -0.036453907426047115], Times[Complex[-0.27630938504679325, 0.26010894184513544], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k]], -1], Subscript[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], k]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta}} | BesselJ(0, z) = (1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi) |
BesselJ[0, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Successful | Successful | - | Failed [4 / 7]
{Complex[0.1024204169391214, -0.20298051839359257] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.35155242920280916, 0.2300320660405755] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}\diff{\theta}} | (1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi) = (1)/(Pi)*int(cos(z*cos(theta)), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cos[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 7] |
| 10.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta}} | BesselJ(n, z) = (1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi) |
BesselJ[n, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta} = \frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\cos@{n\theta}\diff{\theta}} | (1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi) = ((I)^(- n))/(Pi)*int(exp(I*z*cos(theta))*cos(n*theta), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(I)^(- n),Pi]*Integrate[Exp[I*z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 7] | Skipped - Because timed out |
| 10.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | BesselJ(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) |
BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] |
Error | Successful | - | Failed [20 / 35]
{Complex[0.009683985979314524, -0.05759180507972181] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.21993206762171735, 0.08917811286212163] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
| 10.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\cos@{zt}\diff{t}} | (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* cos(z*t), t = 0..1) |
Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[2*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Cos[z*t], {t, 0, 1}, GenerateConditions->None] |
Error | Successful | - | Successful [Tested: 35] |
| 10.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\left(\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}-\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}\right)} | BesselY(nu, z) = (2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*(int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1)- int(exp(- z*t)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity)) |
BesselY[\[Nu], z] == Divide[2*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*(Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}, GenerateConditions->None]- Integrate[Exp[- z*t]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}, GenerateConditions->None]) |
Successful | Successful | - | Failed [15 / 25]
{Complex[-0.9495382353861556, 0.46093572348323536] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1.5]}Complex[-0.7706973036767981, 0.20650772012904162] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 0.5]} |
| 10.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}-\nu t}\diff{t}} | BesselJ(nu, z) = (1)/(Pi)*int(cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*sinh(t)- nu*t), t = 0..infinity) |
BesselJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Failed [1 / 50] 1/50]: [[-.1812319652 <- {nu = -1/2, z = 3/2} |
Skipped - Because timed out |
| 10.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t}+e^{-\nu t}\cos@{\nu\pi}\right)e^{-z\sinh@@{t}}\diff{t}} | BesselY(nu, z) = (1)/(Pi)*int(sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t)+ exp(- nu*t)*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity) |
BesselY[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t]+ Exp[- \[Nu]*t]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}} | BesselJ(nu, x) = (2)/(Pi)*int(sin(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) |
BesselJ[\[Nu], x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}} | BesselY(nu, x) = -(2)/(Pi)*int(cos(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) |
BesselY[\[Nu], x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}}\diff{t}} | BesselJ(0, x) = (2)/(Pi)*int(sin(x*cosh(t)), t = 0..infinity) |
BesselJ[0, x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[t]], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}}\diff{t}} | BesselY(0, x) = -(2)/(Pi)*int(cos(x*cosh(t)), t = 0..infinity) |
BesselY[0, x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\sin@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}} | BesselJ(nu, x) = (2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((sin(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity) |
BesselJ[\[Nu], x] == Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Sin[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None] |
Successful | Error | - | Successful [Tested: 15] |
| 10.9#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{x} = -\frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}} | BesselY(nu, x) = -(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((cos(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity) |
BesselY[\[Nu], x] == -Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Cos[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None] |
Successful | Error | - | Skip - No test values generated |
| 10.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-\pi i}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}} | BesselJ(nu, z) = (1)/(2*Pi*I)*int(exp(z*sinh(t)- nu*t), t = infinity - Pi*I..infinity + Pi*I) |
BesselJ[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, Infinity - Pi*I, Infinity + Pi*I}, GenerateConditions->None] |
Error | Failure | - | Failed [70 / 70]
{Complex[0.4358908643715884, -0.07192294931339177] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.0679098760861825, 0.09257666026367889] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.9#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{1}{\pi i}\int_{-\infty}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}} | HankelH1(nu, z) = (1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity + Pi*I) |
HankelH1[\[Nu], z] == Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity + Pi*I}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = -\frac{1}{\pi i}\int_{-\infty}^{\infty-\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}} | HankelH2(nu, z) = -(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity - Pi*I) |
HankelH2[\[Nu], z] == -Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity - Pi*I}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.9.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{2\pi i}\int_{-\infty}^{(0+)}\exp@{t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}} | BesselJ(nu, z) = (((1)/(2)*z)^(nu))/(2*Pi*I)*int(exp(t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = - infinity..(0 +)) |
BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],2*Pi*I]*Integrate[Exp[t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, - Infinity, (0 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.9.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{\EulerGamma@{\frac{1}{2}-\nu}(\frac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{0}^{(1+)}\cos@{zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | BesselJ(nu, z) = (GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(cos(z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 0..(1 +)) |
BesselJ[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[3,2])* I]*Integrate[Cos[z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 0, (1 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.9#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1+i\infty}^{(1+)}e^{izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | HankelH1(nu, z) = (GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 + I*infinity..(1 +)) |
HankelH1[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[3,2])* I]*Integrate[Exp[I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 + I*Infinity, (1 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.9#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1-i\infty}^{(1+)}e^{-izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}} | HankelH2(nu, z) = (GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(- I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 - I*infinity..(1 +)) |
HankelH2[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[3,2])* I]*Integrate[Exp[- I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 - I*Infinity, (1 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{-\infty-ic}^{-\infty+ic}\frac{\EulerGamma@{t}}{\EulerGamma@{\nu-t+1}}(\tfrac{1}{2}z)^{\nu-2t}\diff{t}} | BesselJ(nu, z) = (1)/(2*Pi*I)*int((GAMMA(t))/(GAMMA(nu - t + 1))*((1)/(2)*z)^(nu - 2*t), t = - infinity - I*c..- infinity + I*c) |
BesselJ[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Divide[Gamma[t],Gamma[\[Nu]- t + 1]]*(Divide[1,2]*z)^(\[Nu]- 2*t), {t, - Infinity - I*c, - Infinity + I*c}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[0.4358908643715884, -0.07192294931339177] <- {Rule[c, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.0679098760861825, 0.09257666026367889] <- {Rule[c, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.9.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = -\frac{e^{-\frac{1}{2}\nu\pi i}}{2\pi^{2}}\*\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(-\tfrac{1}{2}iz)^{\nu-2t}\diff{t}} | HankelH1(nu, z) = -(exp(-(1)/(2)*nu*Pi*I))/(2*(Pi)^(2))* int(GAMMA(t)*GAMMA(t - nu)*(-(1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity) |
HankelH1[\[Nu], z] == -Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]* Integrate[Gamma[t]*Gamma[t - \[Nu]]*(-Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] |
Failure | Error | Failed [120 / 120] 120/120]: [[.2971181619-.8401954886*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-.8661908042+.2691615148*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 10.9.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \frac{e^{\frac{1}{2}\nu\pi i}}{2\pi^{2}}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}iz)^{\nu-2t}\diff{t}} | HankelH2(nu, z) = (exp((1)/(2)*nu*Pi*I))/(2*(Pi)^(2))*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity) |
HankelH2[\[Nu], z] == Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] |
Failure | Error | Failed [120 / 120] 120/120]: [[-.1414870617+.1246394392*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}-.1498748781e-1-.1846515642*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I} |
Skipped - Because timed out |
| 10.9.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\mu}@{z}\BesselJ{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}} | BesselJ(mu, z)*BesselJ(nu, z) = (2)/(Pi)*int(BesselJ(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..Pi/ 2) |
BesselJ[\[Mu], z]*BesselJ[\[Nu], z] == Divide[2,Pi]*Integrate[BesselJ[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Failure | Error | - | Skipped - Because timed out |
| 10.9.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{2\nu}@{2(z\zeta)^{\frac{1}{2}}\sin@@{\theta}}\cos@{(z-\zeta)\cos@@{\theta}}\diff{\theta}} | BesselJ(nu, z)*BesselJ(nu, zeta) = (2)/(Pi)*int(BesselJ(2*nu, 2*(z*zeta)^((1)/(2))* sin(theta))*cos((z - zeta)* cos(theta)), theta = 0..Pi/ 2) |
BesselJ[\[Nu], z]*BesselJ[\[Nu], \[Zeta]] == Divide[2,Pi]*Integrate[BesselJ[2*\[Nu], 2*(z*\[Zeta])^(Divide[1,2])* Sin[\[Theta]]]*Cos[(z - \[Zeta])* Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Failure | Error | - | Skipped - Because timed out |
| 10.9.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp@{\frac{1}{2}t-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselI{\nu}@{\frac{z\zeta}{t}}\frac{\diff{t}}{t}} | BesselJ(nu, z)*BesselJ(nu, zeta) = (1)/(2*Pi*I)*int(* exp((1)/(2)*t -((z)^(2)+ (zeta)^(2))/(2*t))*BesselI(nu, (z*zeta)/(t))*(1)/(t), t = c - I*infinity..c + I*infinity) |
BesselJ[\[Nu], z]*BesselJ[\[Nu], \[Zeta]] == Divide[1,2*Pi*I]*Integrate[* Exp[Divide[1,2]*t -Divide[(z)^(2)+ \[Zeta]^(2),2*t]]*BesselI[\[Nu], Divide[z*\[Zeta],t]]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.9.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}^{2}@{z}+\BesselY{\nu}^{2}@{z} = \frac{8}{\pi^{2}}\int_{0}^{\infty}\cosh@{2\nu t}\modBesselK{0}@{2z\sinh@@{t}}\diff{t}} | (BesselJ(nu, z))^(2)+ (BesselY(nu, z))^(2) = (8)/((Pi)^(2))*int(cosh(2*nu*t)*BesselK(0, 2*z*sinh(t)), t = 0..infinity) |
(BesselJ[\[Nu], z])^(2)+ (BesselY[\[Nu], z])^(2) == Divide[8,(Pi)^(2)]*Integrate[Cosh[2*\[Nu]*t]*BesselK[0, 2*z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\BesselJ{\nu}@{z}} | BesselJ(nu, z*exp(m*Pi*I)) = exp(m*nu*Pi*I)*BesselJ(nu, z) |
BesselJ[\[Nu], z*Exp[m*Pi*I]] == Exp[m*\[Nu]*Pi*I]*BesselJ[\[Nu], z] |
Failure | Failure | Failed [132 / 210] 132/210]: [[-1.978604450-.5916012221*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.4256613630-.5580360922e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [120 / 210]
{Complex[-1.9786044502778974, -0.5916012230349773] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.42566136315461117, -0.05580360945599949] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\BesselY{\nu}@{z}+2i\sin@{m\nu\pi}\cot@{\nu\pi}\BesselJ{\nu}@{z}} | BesselY(nu, z*exp(m*Pi*I)) = exp(- m*nu*Pi*I)*BesselY(nu, z)+ 2*I*sin(m*nu*Pi)*cot(nu*Pi)*BesselJ(nu, z) |
BesselY[\[Nu], z*Exp[m*Pi*I]] == Exp[- m*\[Nu]*Pi*I]*BesselY[\[Nu], z]+ 2*I*Sin[m*\[Nu]*Pi]*Cot[\[Nu]*Pi]*BesselJ[\[Nu], z] |
Failure | Failure | Failed [170 / 210] 170/210]: [[-4.492502702+3.271310776*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}19.72399963+2.416868418*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [162 / 210]
{Complex[-4.49250270148862, 3.2713107749000305] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[19.723999620348792, 2.416868461226219] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\nu\pi}\HankelH{1}{\nu}@{ze^{m\pi i}} = -\sin@{(m-1)\nu\pi}\HankelH{1}{\nu}@{z}-e^{-\nu\pi i}\sin@{m\nu\pi}\HankelH{2}{\nu}@{z}} | sin(nu*Pi)*HankelH1(nu, z*exp(m*Pi*I)) = - sin((m - 1)* nu*Pi)*HankelH1(nu, z)- exp(- nu*Pi*I)*sin(m*nu*Pi)*HankelH2(nu, z) |
Sin[\[Nu]*Pi]*HankelH1[\[Nu], z*Exp[m*Pi*I]] == - Sin[(m - 1)* \[Nu]*Pi]*HankelH1[\[Nu], z]- Exp[- \[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH2[\[Nu], z] |
Failure | Failure | Failed [132 / 210] 132/210]: [[-16.06107638+5.815014709*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}39.27071892+24.34608468*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [120 / 210]
{Complex[-16.061076381218605, 5.815014694873561] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[39.27071883811536, 24.346084784539414] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\nu\pi}\HankelH{2}{\nu}@{ze^{m\pi i}} = e^{\nu\pi i}\sin@{m\nu\pi}\HankelH{1}{\nu}@{z}+\sin@{(m+1)\nu\pi}\HankelH{2}{\nu}@{z}} | sin(nu*Pi)*HankelH2(nu, z*exp(m*Pi*I)) = exp(nu*Pi*I)*sin(m*nu*Pi)*HankelH1(nu, z)+ sin((m + 1)* nu*Pi)*HankelH2(nu, z) |
Sin[\[Nu]*Pi]*HankelH2[\[Nu], z*Exp[m*Pi*I]] == Exp[\[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH1[\[Nu], z]+ Sin[(m + 1)* \[Nu]*Pi]*HankelH2[\[Nu], z] |
Failure | Failure | Failed [132 / 210] 132/210]: [[9.518923666+1.283901315*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}-38.63237633-26.24866521*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [120 / 210]
{Complex[9.518923662743454, 1.2839013369012835] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-38.63237622058036, -26.24866530437453] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{ze^{\pi i}} = -e^{-\nu\pi i}\HankelH{2}{\nu}@{z}} | HankelH1(nu, z*exp(Pi*I)) = - exp(- nu*Pi*I)*HankelH2(nu, z) |
HankelH1[\[Nu], z*Exp[Pi*I]] == - Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z] |
Failure | Failure | Failed [20 / 70] 20/70]: [[-5.249915228-5.084103922*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-3.129030441-5.176244122*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [20 / 70]
{Complex[-5.2499152251779275, -5.084103924523598] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.4609763579335797, 35.01102127779514] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.11#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{ze^{-\pi i}} = -e^{\nu\pi i}\HankelH{1}{\nu}@{z}} | HankelH2(nu, z*exp(- Pi*I)) = - exp(nu*Pi*I)*HankelH1(nu, z) |
HankelH2[\[Nu], z*Exp[- Pi*I]] == - Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z] |
Failure | Failure | Failed [50 / 70] 50/70]: [[1.033334476+.7163604616*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}1.427918302+.5187414665*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I} |
Failed [50 / 70]
{Complex[1.0333344760783634, 0.7163604618419928] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.538721989873022, -0.29666827540401164] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{ze^{m\pi i}} = (-1)^{mn}(\BesselY{n}@{z}+2im\BesselJ{n}@{z})} | BesselY(n, z*exp(m*Pi*I)) = (- 1)^(m*n)*(BesselY(n, z)+ 2*I*m*BesselJ(n, z)) |
BesselY[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)*(BesselY[n, z]+ 2*I*m*BesselJ[n, z]) |
Failure | Failure | Failed [57 / 63] 57/63]: [[-.7553141392+1.723217630*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}.3969469092-.2695422112*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} |
Failed [48 / 63]
{Complex[-0.7553141389736522, 1.7232176296930342] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.39694690825884216, -0.26954221211204654] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{n}@{ze^{m\pi i}} = (-1)^{mn-1}((m-1)\HankelH{1}{n}@{z}+m\HankelH{2}{n}@{z})} | HankelH1(n, z*exp(m*Pi*I)) = (- 1)^(m*n - 1)*((m - 1)*HankelH1(n, z)+ m*HankelH2(n, z)) |
HankelH1[n, z*Exp[m*Pi*I]] == (- 1)^(m*n - 1)*((m - 1)*HankelH1[n, z]+ m*HankelH2[n, z]) |
Failure | Failure | Failed [57 / 63] 57/63]: [[-1.723217630-.7553141394*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}.2695422111+.3969469092*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} |
Failed [48 / 63]
{Complex[-1.7232176296930342, -0.7553141389736522] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.26954221211204654, 0.39694690825884216] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{n}@{ze^{m\pi i}} = (-1)^{mn}(m\HankelH{1}{n}@{z}+(m+1)\HankelH{2}{n}@{z})} | HankelH2(n, z*exp(m*Pi*I)) = (- 1)^(m*n)*(m*HankelH1(n, z)+(m + 1)*HankelH2(n, z)) |
HankelH2[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)*(m*HankelH1[n, z]+(m + 1)*HankelH2[n, z]) |
Failure | Failure | Failed [57 / 63] 57/63]: [[1.723217630+.755314139*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}-.269542211-.396946909*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} |
Failed [48 / 63]
{Complex[1.7232176296930342, 0.7553141389736524] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.26954221211204654, -0.39694690825884216] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.11#E9X | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselJ{\nu}@{\conj{z}} = \conj{\BesselJ{\nu}@{z}}} | BesselJ(nu, conjugate(z)) = conjugate(BesselJ(nu, z)) |
BesselJ[\[Nu], Conjugate[z]] == Conjugate[BesselJ[\[Nu], z]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.11#E9X | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselY{\nu}@{\conj{z}} = \conj{\BesselY{\nu}@{z}}} | BesselY(nu, conjugate(z)) = conjugate(BesselY(nu, z)) |
BesselY[\[Nu], Conjugate[z]] == Conjugate[BesselY[\[Nu], z]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.11#E9Xa | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{1}{\nu}@{\conj{z}} = \conj{\HankelH{2}{\nu}@{z}}} | HankelH1(nu, conjugate(z)) = conjugate(HankelH2(nu, z)) |
HankelH1[\[Nu], Conjugate[z]] == Conjugate[HankelH2[\[Nu], z]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.11#E9Xa | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{2}{\nu}@{\conj{z}} = \conj{\HankelH{1}{\nu}@{z}}} | HankelH2(nu, conjugate(z)) = conjugate(HankelH1(nu, z)) |
HankelH2[\[Nu], Conjugate[z]] == Conjugate[HankelH1[\[Nu], z]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\frac{1}{2}z(t-t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\BesselJ{m}@{z}} | exp((1)/(2)*z*(t - (t)^(- 1))) = sum((t)^(m)* BesselJ(m, z), m = - infinity..infinity) |
Exp[Divide[1,2]*z*(t - (t)^(- 1))] == Sum[(t)^(m)* BesselJ[m, z], {m, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Successful | Successful [Tested: 42] | Successful [Tested: 42] |
| 10.12#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z\sin@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}\BesselJ{2k}@{z}\cos@{2k\theta}} | cos(z*sin(theta)) = BesselJ(0, z)+ 2*sum(BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity) |
Cos[z*Sin[\[Theta]]] == BesselJ[0, z]+ 2*Sum[BesselJ[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Successful | Skipped - Because timed out | Successful [Tested: 70] |
| 10.12#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z\sin@@{\theta}} = 2\sum_{k=0}^{\infty}\BesselJ{2k+1}@{z}\sin@{(2k+1)\theta}} | sin(z*sin(theta)) = 2*sum(BesselJ(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity) |
Sin[z*Sin[\[Theta]]] == 2*Sum[BesselJ[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None] |
Error | Successful | Skipped - Because timed out | Successful [Tested: 70] |
| 10.12#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z\cos@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{2k}@{z}\cos@{2k\theta}} | cos(z*cos(theta)) = BesselJ(0, z)+ 2*sum((- 1)^(k)* BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity) |
Cos[z*Cos[\[Theta]]] == BesselJ[0, z]+ 2*Sum[(- 1)^(k)* BesselJ[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Successful | Skipped - Because timed out | Successful [Tested: 70] |
| 10.12#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z\cos@@{\theta}} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{2k+1}@{z}\cos@{(2k+1)\theta}} | sin(z*cos(theta)) = 2*sum((- 1)^(k)* BesselJ(2*k + 1, z)*cos((2*k + 1)* theta), k = 0..infinity) |
Sin[z*Cos[\[Theta]]] == 2*Sum[(- 1)^(k)* BesselJ[2*k + 1, z]*Cos[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None] |
Error | Successful | Skipped - Because timed out | Successful [Tested: 70] |
| 10.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 = \BesselJ{0}@{z}+2\BesselJ{2}@{z}+2\BesselJ{4}@{z}+2\BesselJ{6}@{z}+\dotsb} | 1 = BesselJ(0, z)+ 2*BesselJ(2, z)+ 2*BesselJ(4, z)+ 2*BesselJ(6, z)+ .. |
1 == BesselJ[0, z]+ 2*BesselJ[2, z]+ 2*BesselJ[4, z]+ 2*BesselJ[6, z]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-9.924736618779559*^-8, -1.6360842739013975*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-9.440290587615918*^-8, -1.7199789187696823*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.12#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \BesselJ{0}@{z}-2\BesselJ{2}@{z}+2\BesselJ{4}@{z}-2\BesselJ{6}@{z}+\dotsb} | cos(z) = BesselJ(0, z)- 2*BesselJ(2, z)+ 2*BesselJ(4, z)- 2*BesselJ(6, z)+ .. |
Cos[z] == BesselJ[0, z]- 2*BesselJ[2, z]+ 2*BesselJ[4, z]- 2*BesselJ[6, z]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-9.976125969757277*^-8, -1.6267640928768756*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-9.384008414770051*^-8, -1.7292990711625933*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.12#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = 2\BesselJ{1}@{z}-2\BesselJ{3}@{z}+2\BesselJ{5}@{z}-\dotsb} | sin(z) = 2*BesselJ(1, z)- 2*BesselJ(3, z)+ 2*BesselJ(5, z)- .. |
Sin[z] == 2*BesselJ[1, z]- 2*BesselJ[3, z]+ 2*BesselJ[5, z]- \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[2.683443869444524*^-6, 1.443280323643048*^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[1.6585570595806232*^-6, -2.68341820086615*^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.12#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}z\cos@@{z} = \BesselJ{1}@{z}-9\BesselJ{3}@{z}+25\BesselJ{5}@{z}-49\BesselJ{7}@{z}+\dotsb} | (1)/(2)*z*cos(z) = BesselJ(1, z)- 9*BesselJ(3, z)+ 25*BesselJ(5, z)- 49*BesselJ(7, z)+ .. |
Divide[1,2]*z*Cos[z] == BesselJ[1, z]- 9*BesselJ[3, z]+ 25*BesselJ[5, z]- 49*BesselJ[7, z]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-1.0583928733431947*^-8, -4.2969798588234076*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[4.4207480831559565*^-7, 1.0857586385526474*^-8], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.12#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}z\sin@@{z} = 4\BesselJ{2}@{z}-16\BesselJ{4}@{z}+36\BesselJ{6}@{z}-\dotsi} | (1)/(2)*z*sin(z) = 4*BesselJ(2, z)- 16*BesselJ(4, z)+ 36*BesselJ(6, z)- .. |
Divide[1,2]*z*Sin[z] == 4*BesselJ[2, z]- 16*BesselJ[4, z]+ 36*BesselJ[6, z]- \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[3.196945008165919*^-6, 5.1972576656234*^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[2.997776089863624*^-6, 5.542144419168338*^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.13.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w} | (w)^(2*n) = (- 1)^(n)* (lambda)^(2*n)* (z)^(- n)* w |
(w)^(2*n) == (- 1)^(n)* \[Lambda]^(2*n)* (z)^(- n)* w |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.13.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0} | ((vartheta)^(4)- 2*((nu)^(2)+ (mu)^(2))*(vartheta)^(2)+((nu)^(2)- (mu)^(2))^(2))* w + 4*(z)^(2)*(vartheta + 1)*(vartheta + 2)* w = 0 |
(\[CurlyTheta]^(4)- 2*(\[Nu]^(2)+ \[Mu]^(2))*\[CurlyTheta]^(2)+(\[Nu]^(2)- \[Mu]^(2))^(2))* w + 4*(z)^(2)*(\[CurlyTheta]+ 1)*(\[CurlyTheta]+ 2)* w == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.14#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{x}| \leq 1} | abs(BesselJ(nu, x)) <= 1 |
Abs[BesselJ[\[Nu], x]] <= 1 |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.14#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{x}| \leq 2^{-\frac{1}{2}}} | abs(BesselJ(nu, x)) <= (2)^(-(1)/(2)) |
Abs[BesselJ[\[Nu], x]] <= (2)^(-Divide[1,2]) |
Failure | Failure | Successful [Tested: 2] | Successful [Tested: 2] |
| 10.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \BesselJ{\nu}@{\nu}} | 0 < BesselJ(nu, nu) |
0 < BesselJ[\[Nu], \[Nu]] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}}} | BesselJ(nu, nu) < ((2)^((1)/(3)))/((3)^((2)/(3))* GAMMA((2)/(3))*(nu)^((1)/(3))) |
BesselJ[\[Nu], \[Nu]] < Divide[(2)^(Divide[1,3]),(3)^(Divide[2,3])* Gamma[Divide[2,3]]*\[Nu]^(Divide[1,3])] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{z}| \leq e^{|\imagpart@@{z}|}} | abs(BesselJ(n, z)) <= exp(abs(Im(z))) |
Abs[BesselJ[n, z]] <= Exp[Abs[Im[z]]] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{z}| \leq \frac{|\tfrac{1}{2}z|^{\nu}e^{|\imagpart@@{z}|}}{\EulerGamma@{\nu+1}}} | abs(BesselJ(nu, z)) <= ((abs((1)/(2)*z))^(nu)* exp(abs(Im(z))))/(GAMMA(nu + 1)) |
Abs[BesselJ[\[Nu], z]] <= Divide[(Abs[Divide[1,2]*z])^\[Nu]* Exp[Abs[Im[z]]],Gamma[\[Nu]+ 1]] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}@{\nu x}| \leq \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}} | abs(BesselJ(nu, nu*x)) <= ((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu)) |
Abs[BesselJ[\[Nu], \[Nu]*x]] <= Divide[(x)^\[Nu]* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^\[Nu]] |
Failure | Failure | Successful [Tested: 3] | Skip - No test values generated |
| 10.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{\nu}'@{\nu x}| \leq \frac{(1+x^{2})^{\frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}} | abs(diff( BesselJ(nu, nu*x), nu*x$(1) )) <= ((1 + (x)^(2))^((1)/(4)))/(x*(2*Pi*nu)^((1)/(2)))*((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu)) |
Abs[D[BesselJ[\[Nu], \[Nu]*x], {\[Nu]*x, 1}]] <= Divide[(1 + (x)^(2))^(Divide[1,4]),x*(2*Pi*\[Nu])^(Divide[1,2])]*Divide[(x)^\[Nu]* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^\[Nu]] |
Error | Failure | - | Skip - No test values generated |
| 10.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}}} | 1 <= (BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu)) |
1 <= Divide[BesselJ[\[Nu], \[Nu]*x],(x)^\[Nu]* BesselJ[\[Nu], \[Nu]]] |
Failure | Failure | Successful [Tested: 3] | Skip - No test values generated |
| 10.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} \leq e^{\nu(1-x)}} | (BesselJ(nu, nu*x))/((x)^(nu)* BesselJ(nu, nu)) <= exp(nu*(1 - x)) |
Divide[BesselJ[\[Nu], \[Nu]*x],(x)^\[Nu]* BesselJ[\[Nu], \[Nu]]] <= Exp[\[Nu]*(1 - x)] |
Failure | Failure | Successful [Tested: 3] | Skip - No test values generated |
| 10.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{nz}| \leq \frac{\left|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}\right|^{n}}} | abs(BesselJ(n, n*z)) <= (abs((z)^(n)* exp(n*(1 - (z)^(2))^((1)/(2)))))/((abs(1 +(1 - (z)^(2))^((1)/(2))))^(n)) |
Abs[BesselJ[n, n*z]] <= Divide[Abs[(z)^(n)* Exp[n*(1 - (z)^(2))^(Divide[1,2])]],(Abs[1 +(1 - (z)^(2))^(Divide[1,2])])^(n)] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\BesselJ{n}@{nz}| \leq 1} | abs(BesselJ(n, n*z)) <= 1 |
Abs[BesselJ[n, n*z]] <= 1 |
Failure | Failure | Error | Successful [Tested: 21] |
| 10.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselJ{+\nu}@{z}}{\nu} = +\BesselJ{+\nu}@{z}\ln@{\tfrac{1}{2}z}-(\tfrac{1}{2}z)^{+\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{k+1+\nu}}{\EulerGamma@{k+1+\nu}}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!}} | diff(BesselJ(+ nu, z), nu) = + BesselJ(+ nu, z)*ln((1)/(2)*z)-((1)/(2)*z)^(+ nu)* sum((- 1)^(k)*(Psi(k + 1 + nu))/(GAMMA(k + 1 + nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselJ[+ \[Nu], z], \[Nu]] == + BesselJ[+ \[Nu], z]*Log[Divide[1,2]*z]-(Divide[1,2]*z)^(+ \[Nu])* Sum[(- 1)^(k)*Divide[PolyGamma[k + 1 + \[Nu]],Gamma[k + 1 + \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [7 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -2]} |
| 10.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselJ{-\nu}@{z}}{\nu} = -\BesselJ{-\nu}@{z}\ln@{\tfrac{1}{2}z}+(\tfrac{1}{2}z)^{-\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{k+1-\nu}}{\EulerGamma@{k+1-\nu}}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!}} | diff(BesselJ(- nu, z), nu) = - BesselJ(- nu, z)*ln((1)/(2)*z)+((1)/(2)*z)^(- nu)* sum((- 1)^(k)*(Psi(k + 1 - nu))/(GAMMA(k + 1 - nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselJ[- \[Nu], z], \[Nu]] == - BesselJ[- \[Nu], z]*Log[Divide[1,2]*z]+(Divide[1,2]*z)^(- \[Nu])* Sum[(- 1)^(k)*Divide[PolyGamma[k + 1 - \[Nu]],Gamma[k + 1 - \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [7 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 2]} |
| 10.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselY{\nu}@{z}}{\nu} = \cot@{\nu\pi}\left(\pderiv{\BesselJ{\nu}@{z}}{\nu}-\pi\BesselY{\nu}@{z}\right)-\csc@{\nu\pi}\pderiv{\BesselJ{-\nu}@{z}}{\nu}-\pi\BesselJ{\nu}@{z}} | diff(BesselY(nu, z), nu) = cot(nu*Pi)*(diff(BesselJ(nu, z), nu)- Pi*BesselY(nu, z))- csc(nu*Pi)*diff(BesselJ(- nu, z), nu)- Pi*BesselJ(nu, z) |
D[BesselY[\[Nu], z], \[Nu]] == Cot[\[Nu]*Pi]*(D[BesselJ[\[Nu], z], \[Nu]]- Pi*BesselY[\[Nu], z])- Csc[\[Nu]*Pi]*D[BesselJ[- \[Nu], z], \[Nu]]- Pi*BesselJ[\[Nu], z] |
Successful | Failure | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.16#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{1}{2}}@{z} = \BesselY{-\frac{1}{2}}@{z}} | BesselJ((1)/(2), z) = BesselY(-(1)/(2), z) |
BesselJ[Divide[1,2], z] == BesselY[-Divide[1,2], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.16#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sin@@{z}} | BesselY(-(1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* sin(z) |
BesselY[-Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Sin[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.16#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-\frac{1}{2}}@{z} = -\BesselY{\frac{1}{2}}@{z}} | BesselJ(-(1)/(2), z) = - BesselY((1)/(2), z) |
BesselJ[-Divide[1,2], z] == - BesselY[Divide[1,2], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.16#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\BesselY{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\cos@@{z}} | - BesselY((1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* cos(z) |
- BesselY[Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Cos[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.16#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\frac{1}{2}}@{z} = -i\HankelH{1}{-\frac{1}{2}}@{z}} | HankelH1((1)/(2), z) = - I*HankelH1(-(1)/(2), z) |
HankelH1[Divide[1,2], z] == - I*HankelH1[-Divide[1,2], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.16#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -i\HankelH{1}{-\frac{1}{2}}@{z} = -i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{iz}} | - I*HankelH1(-(1)/(2), z) = - I*((2)/(Pi*z))^((1)/(2))* exp(I*z) |
- I*HankelH1[-Divide[1,2], z] == - I*(Divide[2,Pi*z])^(Divide[1,2])* Exp[I*z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.16#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\frac{1}{2}}@{z} = i\HankelH{2}{-\frac{1}{2}}@{z}} | HankelH2((1)/(2), z) = I*HankelH2(-(1)/(2), z) |
HankelH2[Divide[1,2], z] == I*HankelH2[-Divide[1,2], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.16#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\HankelH{2}{-\frac{1}{2}}@{z} = i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{-iz}} | I*HankelH2(-(1)/(2), z) = I*((2)/(Pi*z))^((1)/(2))* exp(- I*z) |
I*HankelH2[-Divide[1,2], z] == I*(Divide[2,Pi*z])^(Divide[1,2])* Exp[- I*z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.16#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{1}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(\paraW@{0}{2z^{\frac{1}{2}}}-\paraW@{0}{-2z^{\frac{1}{2}}}\right)} | Error |
BesselJ[Divide[1,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[1,4])*(Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] )- Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), - 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), - 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] )) |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[0.8427727646508262, -0.04212015747529019], Times[Complex[0.4703662267003617, -0.06192488852586185], Plus[Times[0.4550898605622274, Plus[Times[Complex[0.3150667711363517, -1.1318933470332309], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.1941072423227021, 0.35884759380625464], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[1.684848183162187, 0.4798071226199044], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.8058077119758371, -1.0109338182195815], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.7942814592773979, 0.6544287188687908], Times[Complex[0.41086410074312574, -0.23721249916439713], Plus[Times[0.4550898605622274, Plus[Times[Complex[1.9382359752879499, -0.7976721648462198], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.22978077998995444, -0.1584303699393873], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[0.8690225748967872, 1.5500248253586082], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[2.5774777701947826, 0.910783030451775], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.16#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}-\paraW'@{0}{-2z^{\frac{1}{2}}}\right)} | Error |
BesselJ[Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])*((D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 2*(z)^(Divide[1,2]))- (D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> - 2*(z)^(Divide[1,2]))) |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[0.5824093961234496, 0.15854248220296385], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.0836786417162193, 0.6909849218136797], Times[Complex[0.0, -0.4744249983287943], Plus[Times[-0.4550898605622274, Plus[Times[Complex[-1.52733809531001, -0.015580244977093649], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-1.3790215645615536, -1.2403191305633965], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[-0.154282678975249, -1.0920025998149403], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.302599209723706, 0.13273628577136276], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.16#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}+\paraW'@{0}{-2z^{\frac{1}{2}}}\right)} | Error |
BesselJ[-Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])*((D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 2*(z)^(Divide[1,2]))+ (D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> - 2*(z)^(Divide[1,2]))) |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[0.05605283808026881, -0.4145839244466886], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.44186162583484034, -0.6708696264637843], Times[Complex[0.0, -0.4744249983287943], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.52733809531001, -0.015580244977093649], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-1.3790215645615536, -1.2403191305633965], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[-0.154282678975249, -1.0920025998149403], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.302599209723706, 0.13273628577136276], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2iz}} | BesselJ(nu, z) = (((1)/(2)*z)^(nu)* exp(- I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, + 2*I*z) |
BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu]* Exp[- I*z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, + 2*I*z] |
Failure | Successful | Failed [7 / 56] 7/56]: [[-.827986137e-1+.7317301038*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}-.8060140108+.3257248263*I <- {nu = -1/2, z = -1/2+1/2*I*3^(1/2)} |
Failed [7 / 56]
{Complex[-0.08279861346468581, 0.7317301035002939] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}Complex[-0.8060140105131326, 0.32572482654389856] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]} |
| 10.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{+ iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{- 2iz}} | BesselJ(nu, z) = (((1)/(2)*z)^(nu)* exp(+ I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, - 2*I*z) |
BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu]* Exp[+ I*z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, - 2*I*z] |
Failure | Successful | Failed [7 / 56] 7/56]: [[.827986132e-1-.7317301035*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}.8060140102-.3257248264*I <- {nu = -1/2, z = -1/2+1/2*I*3^(1/2)} |
Failed [7 / 56]
{Complex[0.08279861346468548, -0.7317301035002935] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}Complex[0.8060140105131325, -0.325724826543898] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]} |
| 10.16.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{e^{-(2\nu+1)\pi i/4}}{2^{2\nu}\EulerGamma@{\nu+1}}(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{+ 2iz}} | BesselJ(nu, z) = (exp(-(2*nu + 1)* Pi*I/ 4))/((2)^(2*nu)* GAMMA(nu + 1))*(2*z)^(-(1)/(2))* WhittakerM(0, nu, + 2*I*z) |
BesselJ[\[Nu], z] == Divide[Exp[-(2*\[Nu]+ 1)* Pi*I/ 4],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]]*(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], + 2*I*z] |
Failure | Failure | Failed [1 / 7] 1/7]: [[1.448710179-.1398527410*I <- {z = -1/2+1/2*I*3^(1/2), nu = 1/4} |
Failed [1 / 7]
{Complex[1.448710178146189, -0.13985274040860685] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Rational[1, 4]]} |
| 10.16.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{e^{+(2\nu+1)\pi i/4}}{2^{2\nu}\EulerGamma@{\nu+1}}(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{- 2iz}} | BesselJ(nu, z) = (exp(+(2*nu + 1)* Pi*I/ 4))/((2)^(2*nu)* GAMMA(nu + 1))*(2*z)^(-(1)/(2))* WhittakerM(0, nu, - 2*I*z) |
BesselJ[\[Nu], z] == Divide[Exp[+(2*\[Nu]+ 1)* Pi*I/ 4],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]]*(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], - 2*I*z] |
Failure | Failure | Failed [1 / 7] 1/7]: [[1.191860674-.595668984e-1*I <- {z = -1/2*3^(1/2)-1/2*I, nu = 1/4} |
Failed [1 / 7]
{Complex[1.191860673767867, -0.059566897950845576] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Rational[1, 4]]} |
| 10.16.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+1}}\genhyperF{0}{1}@{-}{\nu+1}{-\tfrac{1}{4}z^{2}}} | BesselJ(nu, z) = (((1)/(2)*z)^(nu))/(GAMMA(nu + 1))*hypergeom([-], [nu + 1], -(1)/(4)*(z)^(2)) |
BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+ 1]]*HypergeometricPFQ[{-}, {\[Nu]+ 1}, -Divide[1,4]*(z)^(2)] |
Error | Failure | - | Error |
| 10.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{\frac{1}{2}} = \exp@{\tfrac{1}{2}\ln@@{|z|}+\tfrac{1}{2}i\phase@@{z}}} | (z)^((1)/(2)) = exp((1)/(2)*ln(abs(z))+(1)/(2)*I*argument(z)) |
(z)^(Divide[1,2]) == Exp[Divide[1,2]*Log[Abs[z]]+Divide[1,2]*I*Arg[z]] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.17.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}} | (exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z) = (exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z) |
Error |
Successful | Error | - | - |
| 10.18#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}}} | Error |
Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((BesselJ[\[Nu], x])^(2)+ (BesselY[\[Nu], x])^(2))^(Divide[1,2]) |
Error | Failure | - | Failed [30 / 30]
{Complex[0.19554332981034928, -0.3390785475644471] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.7197518351343698, 1.0182547128018542] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.18#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}}} | Error |
Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((D[BesselJ[\[Nu], x], {x, 1}])^(2)+ (D[BesselY[\[Nu], x], {x, 1}])^(2))^(Divide[1,2]) |
Error | Failure | - | Failed [30 / 30]
{Complex[-0.3065654786420606, 0.09106250304027241] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.41179972752410343, -0.08651542233456301] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.20.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{\zeta}{z}\right)^{2} = \frac{1-z^{2}}{\zeta z^{2}}} | (diff(zeta, z))^(2) = (1 - (z)^(2))/(zeta*(z)^(2)) |
(D[\[Zeta], z])^(2) == Divide[1 - (z)^(2),\[Zeta]*(z)^(2)] |
Failure | Failure | Failed [70 / 70] 70/70]: [[.8660254030+.4999999994*I <- {z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}.4999999994-.8660254030*I <- {z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)} |
Failed [70 / 70]
{Complex[0.8660254037844386, 0.4999999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.4999999999999999, -0.8660254037844386] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.20.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{3}(-\zeta)^{\frac{3}{2}} = \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t}} | (2)/(3)*(- zeta)^((3)/(2)) = int((sqrt((t)^(2)- 1))/(t), t = 1..z) |
Divide[2,3]*(- \[Zeta])^(Divide[3,2]) == Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None] |
Failure | Error | Failed [20 / 20] 20/20]: [[-.7483698391+.4714045210*I <- {z = 3/2, zeta = 1/2*3^(1/2)+1/2*I}-.2769653183-.6666666667*I <- {z = 3/2, zeta = -1/2+1/2*I*3^(1/2)} |
Failed [20 / 20]
{Complex[-0.7483698389729962, 0.4714045207910317] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.27696531818196457, -0.6666666666666666] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.20.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t} = \sqrt{z^{2}-1}-\asec@@{z}} | int((sqrt((t)^(2)- 1))/(t), t = 1..z) = sqrt((z)^(2)- 1)- arcsec(z) |
Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None] == Sqrt[(z)^(2)- 1]- ArcSec[z] |
Failure | Error | Successful [Tested: 2] | Successful [Tested: 2] |
| 10.20#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}(0) = 1} | A[0]*(0) = 1 |
Subscript[A, 0]*(0) == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}(0) = -\tfrac{1}{225}} | A[1]*(0) = -(1)/(225) |
Subscript[A, 1]*(0) == -Divide[1,225] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}(0) = \tfrac{1\;51439}{2182\;95000}} | A[2]*(0) = (151439)/(218295000) |
Subscript[A, 2]*(0) == Divide[151439,218295000] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}(0) = -\tfrac{8872\;78009}{250\;49351\;25000}} | A[3]*(0) = -(887278009)/(2504935125000) |
Subscript[A, 3]*(0) == -Divide[887278009,2504935125000] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}(0) = \tfrac{1}{70}2^{\frac{1}{3}}} | B[0]*(0) = (1)/(70)*(2)^((1)/(3)) |
Subscript[B, 0]*(0) == Divide[1,70]*(2)^(Divide[1,3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}(0) = -\tfrac{1213}{10\;23750}2^{\frac{1}{3}}} | B[1]*(0) = -(1213)/(1023750)*(2)^((1)/(3)) |
Subscript[B, 1]*(0) == -Divide[1213,1023750]*(2)^(Divide[1,3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}(0) = \tfrac{1\;65425\;37833}{3774\;32055\;00000}2^{\frac{1}{3}}} | B[2]*(0) = (16542537833)/(37743205500000)*(2)^((1)/(3)) |
Subscript[B, 2]*(0) == Divide[16542537833,37743205500000]*(2)^(Divide[1,3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3}(0) = -\tfrac{959\;71711\;84603}{25\;47666\;37125\;00000}2^{\frac{1}{3}}} | B[3]*(0) = -(9597171184603)/(25476663712500000)*(2)^((1)/(3)) |
Subscript[B, 3]*(0) == -Divide[9597171184603,25476663712500000]*(2)^(Divide[1,3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = (\tfrac{3}{2})^{\frac{2}{3}}(\tau- i\pi)^{\frac{2}{3}}} | zeta = ((3)/(2))^((2)/(3))*(tau - I*Pi)^((2)/(3)) |
\[Zeta] == (Divide[3,2])^(Divide[2,3])*(\[Tau]- I*Pi)^(Divide[2,3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = e^{- i\pi/3}\tau} | zeta = exp(- I*Pi/ 3)*tau |
\[Zeta] == Exp[- I*Pi/ 3]*\[Tau] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.20.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = +(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}+\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}} | z = +(tau*coth(tau)- (tau)^(2))^((1)/(2))+ I*((tau)^(2)- tau*tanh(tau))^((1)/(2)) |
z == +(\[Tau]*Coth[\[Tau]]- \[Tau]^(2))^(Divide[1,2])+ I*(\[Tau]^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2]) |
Failure | Failure | Failed [21 / 21] 21/21]: [[.8660254040-1.214547924*I <- {tau = 3/2, z = 1/2*3^(1/2)+1/2*I}-.5000000000-.8485225201*I <- {tau = 3/2, z = -1/2+1/2*I*3^(1/2)} |
Skip - No test values generated |
| 10.20.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = -(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}-\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}} | z = -(tau*coth(tau)- (tau)^(2))^((1)/(2))- I*((tau)^(2)- tau*tanh(tau))^((1)/(2)) |
z == -(\[Tau]*Coth[\[Tau]]- \[Tau]^(2))^(Divide[1,2])- I*(\[Tau]^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2]) |
Failure | Failure | Failed [21 / 21] 21/21]: [[.8660254040+2.214547924*I <- {tau = 3/2, z = 1/2*3^(1/2)+1/2*I}-.5000000000+2.580573328*I <- {tau = 3/2, z = -1/2+1/2*I*3^(1/2)} |
Skip - No test values generated |
| 10.21#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{\nu}(0) = 0} | rho[nu]*(0) = 0 |
Subscript[\[Rho], \[Nu]]*(0) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\rho_{\nu}^{2}\deriv{\rho_{\nu}}{t}\deriv[3]{\rho_{\nu}}{t}-3\rho_{\nu}^{2}\*\left(\deriv[2]{\rho_{\nu}}{t}\right)^{2}-4\pi^{2}\rho_{\nu}^{2}\*\left(\deriv{\rho_{\nu}}{t}\right)^{2}+(4\rho_{\nu}^{2}+1-4\nu^{2})\left(\deriv{\rho_{\nu}}{t}\right)^{4} = 0} | 2*(rho[nu])^(2)*diff(rho[nu], t)*diff(rho[nu], [t$(3)])- 3*(rho[nu])^(2)*(diff(rho[nu], [t$(2)]))^(2)- 4*(Pi)^(2)* (rho[nu])^(2)*(diff(rho[nu], t))^(2)(4*rho(rho[nu])^(2)+ 1 - 4*(nu)^(2))*(diff(rho[nu], t))^(4) = 0 |
2*(Subscript[\[Rho], \[Nu]])^(2)*D[Subscript[\[Rho], \[Nu]], t]*D[Subscript[\[Rho], \[Nu]], {t, 3}]- 3*(Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], {t, 2}])^(2)- 4*(Pi)^(2)* (Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], t])^(2)(4*\[Rho](Subscript[\[Rho], \[Nu]])^(2)+ 1 - 4*\[Nu]^(2))*(D[Subscript[\[Rho], \[Nu]], t])^(4) == 0 |
Successful | Successful | - | Successful [Tested: 300] |
| 10.21.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}} | diff(c, nu) = 2*c*int(BesselK(0, 2*c*sinh(t))*exp(- 2*nu*t), t = 0..infinity) |
D[c, \[Nu]] == 2*c*Integrate[BesselK[0, 2*c*Sinh[t]]*Exp[- 2*\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.21#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{0} = 1} | alpha[0] = 1 |
Subscript[\[Alpha], 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \alpha} | alpha[1] = alpha |
Subscript[\[Alpha], 1] == \[Alpha] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2} = \tfrac{3}{10}\alpha^{2}} | alpha[2] = (3)/(10)*(alpha)^(2) |
Subscript[\[Alpha], 2] == Divide[3,10]*\[Alpha]^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{3} = -\tfrac{1}{350}\alpha^{3}+\tfrac{1}{70}} | alpha[3] = -(1)/(350)*(alpha)^(3)+(1)/(70) |
Subscript[\[Alpha], 3] == -Divide[1,350]*\[Alpha]^(3)+Divide[1,70] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{4} = -\tfrac{479}{63000}\alpha^{4}-\tfrac{1}{3150}\alpha} | alpha[4] = -(479)/(63000)*(alpha)^(4)-(1)/(3150)*alpha |
Subscript[\[Alpha], 4] == -Divide[479,63000]*\[Alpha]^(4)-Divide[1,3150]*\[Alpha] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{5} = \tfrac{20231}{80\;85000}\alpha^{5}-\tfrac{551}{1\;61700}\alpha^{2}} | alpha[5] = (20231)/(8085000)*(alpha)^(5)-(551)/(161700)*(alpha)^(2) |
Subscript[\[Alpha], 5] == Divide[20231,8085000]*\[Alpha]^(5)-Divide[551,161700]*\[Alpha]^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21.E46 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \tfrac{1}{2}\ln@@{3}} | a = (1)/(2)*ln(3) |
a == Divide[1,2]*Log[3] |
Failure | Failure | Failed [6 / 6] 6/6]: [[-2.049306144 <- {a = -3/2}.9506938555 <- {a = 3/2} |
Failed [6 / 6]
{-2.049306144334055 <- {Rule[a, -1.5]}0.9506938556659451 <- {Rule[a, 1.5]} |
| 10.21.E46 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\ln@@{3} = 0.54931\dotsc} | (1)/(2)*ln(3) = 0.54931 .. |
Divide[1,2]*Log[3] == 0.54931 \[Ellipsis] |
Error | Failure | Skip - symbolical successful subtest | Failed [1 / 1]
{Plus[0.5493061443340549, Times[-0.54931, …]] <- {} |
| 10.21#Ex51 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{(m-1)\pi}{\lambda-1}} | alpha = ((m - 1)* Pi)/(lambda - 1) |
\[Alpha] == Divide[(m - 1)* Pi,\[Lambda]- 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex52 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{\mu+3}{8\lambda}} | p = (mu + 3)/(8*lambda) |
p == Divide[\[Mu]+ 3,8*\[Lambda]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex53 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = \frac{(\mu^{2}+46\mu-63)(\lambda^{3}-1)}{6(4\lambda)^{3}(\lambda-1)}} | q = (((mu)^(2)+ 46*mu - 63)*((lambda)^(3)- 1))/(6*(4*lambda)^(3)*(lambda - 1)) |
q == Divide[(\[Mu]^(2)+ 46*\[Mu]- 63)*(\[Lambda]^(3)- 1),6*(4*\[Lambda])^(3)*(\[Lambda]- 1)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex54 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)(\lambda^{5}-1)}{5(4\lambda)^{5}(\lambda-1)}} | r = (((mu)^(3)+ 185*(mu)^(2)- 2053*mu + 1899)*((lambda)^(5)- 1))/(5*(4*lambda)^(5)*(lambda - 1)) |
r == Divide[(\[Mu]^(3)+ 185*\[Mu]^(2)- 2053*\[Mu]+ 1899)*(\[Lambda]^(5)- 1),5*(4*\[Lambda])^(5)*(\[Lambda]- 1)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex55 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{(m-\tfrac{1}{2})\pi}{\lambda-1}} | alpha = ((m -(1)/(2))* Pi)/(lambda - 1) |
\[Alpha] == Divide[(m -Divide[1,2])* Pi,\[Lambda]- 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex56 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{(\mu+3)\lambda-(\mu-1)}{8\lambda(\lambda-1)}} | p = ((mu + 3)* lambda -(mu - 1))/(8*lambda*(lambda - 1)) |
p == Divide[(\[Mu]+ 3)* \[Lambda]-(\[Mu]- 1),8*\[Lambda]*(\[Lambda]- 1)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex57 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = \frac{(\mu^{2}+46\mu-63)\lambda^{3}-(\mu-1)(\mu-25)}{6(4\lambda)^{3}(\lambda-1)}} | q = (((mu)^(2)+ 46*mu - 63)* (lambda)^(3)-(mu - 1)*(mu - 25))/(6*(4*lambda)^(3)*(lambda - 1)) |
q == Divide[(\[Mu]^(2)+ 46*\[Mu]- 63)* \[Lambda]^(3)-(\[Mu]- 1)*(\[Mu]- 25),6*(4*\[Lambda])^(3)*(\[Lambda]- 1)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.21#Ex58 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)\lambda^{5}-(\mu-1)(\mu^{2}-114\mu+1073)}{5(4\lambda)^{5}(\lambda-1)}} | r = (((mu)^(3)+ 185*(mu)^(2)- 2053*mu + 1899)* (lambda)^(5)-(mu - 1)*((mu)^(2)- 114*mu + 1073))/(5*(4*lambda)^(5)*(lambda - 1)) |
r == Divide[(\[Mu]^(3)+ 185*\[Mu]^(2)- 2053*\[Mu]+ 1899)* \[Lambda]^(5)-(\[Mu]- 1)*(\[Mu]^(2)- 114*\[Mu]+ 1073),5*(4*\[Lambda])^(5)*(\[Lambda]- 1)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.22.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\diff{t} = 2\sum_{k=0}^{\infty}\BesselJ{\nu+2k+1}@{x}} | int(BesselJ(nu, t), t = 0..x) = 2*sum(BesselJ(nu + 2*k + 1, x), k = 0..infinity) |
Integrate[BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == 2*Sum[BesselJ[\[Nu]+ 2*k + 1, x], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Failed [2 / 24] 2/24]: [[-.277492396 <- {nu = -1/2, x = 3/2}-.1653166018 <- {nu = 1/2, x = 3/2} |
Skipped - Because timed out |
| 10.22.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{2n}@{t}\diff{t} = \int_{0}^{x}\BesselJ{0}@{t}\diff{t}-2\sum_{k=0}^{n-1}\BesselJ{2k+1}@{x},\quad\int_{0}^{x}\BesselJ{2n+1}@{t}\diff{t}} | int(BesselJ(2*n, t), t = 0..x) = int(BesselJ(0, t), t = 0..x)- 2*sum(BesselJ(2*k + 1, x), k = 0..n - 1), int(BesselJ(2*n + 1, t), t = 0..x) |
Integrate[BesselJ[2*n, t], {t, 0, x}, GenerateConditions->None] == Integrate[BesselJ[0, t], {t, 0, x}, GenerateConditions->None]- 2*Sum[BesselJ[2*k + 1, x], {k, 0, n - 1}, GenerateConditions->None], Integrate[BesselJ[2*n + 1, t], {t, 0, x}, GenerateConditions->None] |
Failure | Failure | Error | Error |
| 10.22.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{0}@{t}\diff{t}-2\sum_{k=0}^{n-1}\BesselJ{2k+1}@{x},\quad\int_{0}^{x}\BesselJ{2n+1}@{t}\diff{t} = 1-\BesselJ{0}@{x}-2\sum_{k=1}^{n}\BesselJ{2k}@{x}} | int(BesselJ(0, t), t = 0..x)- 2*sum(BesselJ(2*k + 1, x), k = 0..n - 1), int(BesselJ(2*n + 1, t), t = 0..x) = 1 - BesselJ(0, x)- 2*sum(BesselJ(2*k, x), k = 1..n) |
Integrate[BesselJ[0, t], {t, 0, x}, GenerateConditions->None]- 2*Sum[BesselJ[2*k + 1, x], {k, 0, n - 1}, GenerateConditions->None], Integrate[BesselJ[2*n + 1, t], {t, 0, x}, GenerateConditions->None] == 1 - BesselJ[0, x]- 2*Sum[BesselJ[2*k, x], {k, 1, n}, GenerateConditions->None] |
Failure | Failure | Error | Error |
| 10.22.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = x^{\mu}\frac{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(\nu+2k+1)\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}+k}}{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{2}+k}}\BesselJ{\nu+2k+1}@{x}} | int((t)^(mu)* BesselJ(nu, t), t = 0..x) = (x)^(mu)*(GAMMA((1)/(2)*nu +(1)/(2)*mu +(1)/(2)))/(GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)))* sum(((nu + 2*k + 1)* GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)+ k))/(GAMMA((1)/(2)*nu +(1)/(2)*mu +(3)/(2)+ k))*BesselJ(nu + 2*k + 1, x), k = 0..infinity) |
Integrate[(t)^\[Mu]* BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == (x)^\[Mu]*Divide[Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[1,2]],Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]]* Sum[Divide[(\[Nu]+ 2*k + 1)* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]+ k],Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[3,2]+ k]]*BesselJ[\[Nu]+ 2*k + 1, x], {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.22.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\BesselJ{k}@{x}} | int((1 - BesselJ(0, t))/(t), t = 0..x) = (1)/(2)*sum((Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselJ(k, x), k = 1..infinity) |
Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*Sum[Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselJ[k, x], {k, 1, Infinity}, GenerateConditions->None] |
Error | Failure | Successful [Tested: 3] | Failed [3 / 3]
{Plus[0.2622772441151432, Times[-0.5, NSum[Times[Power[0.75, k], BesselJ[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}Plus[0.03100698635091531, Times[-0.5, NSum[Times[Power[0.25, k], BesselJ[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]} |
| 10.22.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = 2\sum_{k=0}^{\infty}(2k+3)(\digamma@{k+2}-\digamma@{1})\BesselJ{2k+3}@{x}} | x*int((1 - BesselJ(0, t))/(t), t = 0..x) = 2*sum((2*k + 3)*(Psi(k + 2)- Psi(1))* BesselJ(2*k + 3, x), k = 0..infinity) |
x*Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == 2*Sum[(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselJ[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 3] | Skipped - Because timed out |
| 10.22.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}} | int(BesselJ(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*BesselJ(nu + mu, z)*BesselJ(nu - mu, z) |
Integrate[BesselJ[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z] |
Failure | Failure | - | Skipped - Because timed out |
| 10.22.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \pi\cos@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}} | int(BesselJ(2*nu, 2*z*sin(theta))*cos(2*mu*theta), theta = 0..Pi) = Pi*cos(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z) |
Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Pi*Cos[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z] |
Failure | Failure | - | Skipped - Because timed out |
| 10.22.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\sin@{2\mu\theta}\diff{\theta} = \pi\sin@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}} | int(BesselJ(2*nu, 2*z*sin(theta))*sin(2*mu*theta), theta = 0..Pi) = Pi*sin(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z) |
Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Sin[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Pi*Sin[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z] |
Failure | Failure | - | Skipped - Because timed out |
| 10.22.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}^{2}@{z}} | int(BesselJ(0, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*(BesselJ(n, z))^(2) |
Integrate[BesselJ[0, 2*z*Sin[\[Theta]]]*Cos[2*n*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*(BesselJ[n, z])^(2) |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.22.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\cot@{2\nu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}-\tfrac{1}{2}\pi\csc@{2\nu\pi}\BesselJ{\mu-\nu}@{z}\BesselJ{-\mu-\nu}@{z}} | int(BesselY(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*cot(2*nu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)-(1)/(2)*Pi*csc(2*nu*Pi)*BesselJ(mu - nu, z)*BesselJ(- mu - nu, z) |
Integrate[BesselY[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*Cot[2*\[Nu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]-Divide[1,2]*Pi*Csc[2*\[Nu]*Pi]*BesselJ[\[Mu]- \[Nu], z]*BesselJ[- \[Mu]- \[Nu], z] |
Failure | Failure | Error | Skip - No test values generated |
| 10.22.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}@{z}\BesselY{n}@{z}} | int(BesselY(0, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*BesselJ(n, z)*BesselY(n, z) |
Integrate[BesselY[0, 2*z*Sin[\[Theta]]]*Cos[2*n*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*BesselJ[n, z]*BesselY[n, z] |
Failure | Failure | Successful [Tested: 7] | Skipped - Because timed out |
| 10.22.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = 2^{\nu}\EulerGamma@{\nu+1}z^{-\nu-1}\BesselJ{\mu+\nu+1}@{z}} | int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu + 1)*(cos(theta))^(2*nu + 1), theta = 0..(1)/(2)*Pi) = (2)^(nu)* GAMMA(nu + 1)*(z)^(- nu - 1)* BesselJ(mu + nu + 1, z) |
Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^(\[Mu]+ 1)*(Cos[\[Theta]])^(2*\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (2)^\[Nu]* Gamma[\[Nu]+ 1]*(z)^(- \[Nu]- 1)* BesselJ[\[Mu]+ \[Nu]+ 1, z] |
Successful | Error | - | Successful [Tested: 300] |
| 10.22.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}^{2}@{\tfrac{1}{2}z}} | int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi) = (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*(BesselJ(mu, (1)/(2)*z))^(2) |
Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^\[Mu]*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*(BesselJ[\[Mu], Divide[1,2]*z])^(2) |
Successful | Error | - | Successful [Tested: 35] |
| 10.22.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}@{\tfrac{1}{2}z}\BesselY{\mu}@{\tfrac{1}{2}z}} | int(BesselY(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi) = (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*BesselJ(mu, (1)/(2)*z)*BesselY(mu, (1)/(2)*z) |
Integrate[BesselY[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^\[Mu]*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*BesselJ[\[Mu], Divide[1,2]*z]*BesselY[\[Mu], Divide[1,2]*z] |
Successful | Error | - | Skipped - Because timed out |
| 10.22.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\alpha-1}\sec@@{\theta}\diff{\theta} = \frac{(\mu+\nu+\alpha)\EulerGamma@{\mu+\alpha}2^{\alpha-1}}{\nu\EulerGamma@{\mu+1}z^{\alpha}}\BesselJ{\mu+\nu+\alpha}@{z}} | int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*(sin(theta))^(2*alpha - 1)* sec(theta), theta = 0..(1)/(2)*Pi) = ((mu + nu + alpha)* GAMMA(mu + alpha)*(2)^(alpha - 1))/(nu*GAMMA(mu + 1)*(z)^(alpha))*BesselJ(mu + nu + alpha, z) |
Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*(Sin[\[Theta]])^(2*\[Alpha]- 1)* Sec[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu]+ \[Alpha])* Gamma[\[Mu]+ \[Alpha]]*(2)^(\[Alpha]- 1),\[Nu]*Gamma[\[Mu]+ 1]*(z)^\[Alpha]]*BesselJ[\[Mu]+ \[Nu]+ \[Alpha], z] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.22.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}\cot@@{\theta}\diff{\theta} = \tfrac{1}{2}\mu^{-1}\BesselJ{\mu+\nu}@{z}} | int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*cot(theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*(mu)^(- 1)* BesselJ(mu + nu, z) |
Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*Cot[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*\[Mu]^(- 1)* BesselJ[\[Mu]+ \[Nu], z] |
Failure | Error | Skipped - Because timed out | Skip - No test values generated |
| 10.22.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\modBesselI{\nu}@{z\cos@@{\theta}}(\tan@@{\theta})^{\mu+1}\diff{\theta} = \frac{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu}(\tfrac{1}{2}z)^{\mu}}{2\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1}}\BesselJ{\nu}@{z}} | int(BesselJ(mu, z*sin(theta))*BesselI(nu, z*cos(theta))*(tan(theta))^(mu + 1), theta = 0..(1)/(2)*Pi) = (GAMMA((1)/(2)*nu -(1)/(2)*mu)*((1)/(2)*z)^(mu))/(2*GAMMA((1)/(2)*nu +(1)/(2)*mu + 1))*BesselJ(nu, z) |
Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*BesselI[\[Nu], z*Cos[\[Theta]]]*(Tan[\[Theta]])^(\[Mu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]]*(Divide[1,2]*z)^\[Mu],2*Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+ 1]]*BesselJ[\[Nu], z] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.22.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\BesselJ{\nu-1}^{2}@{t}\diff{t} = 2\sum_{k=0}^{\infty}(\nu+2k)\BesselJ{\nu+2k}^{2}@{x}} | int(t*(BesselJ(nu - 1, t))^(2), t = 0..x) = 2*sum((nu + 2*k)* (BesselJ(nu + 2*k, x))^(2), k = 0..infinity) |
Integrate[t*(BesselJ[\[Nu]- 1, t])^(2), {t, 0, x}, GenerateConditions->None] == 2*Sum[(\[Nu]+ 2*k)* (BesselJ[\[Nu]+ 2*k, x])^(2), {k, 0, Infinity}, GenerateConditions->None] |
Failure | Successful | Successful [Tested: 15] | Successful [Tested: 15] |
| 10.22.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\left(\BesselJ{\nu-1}^{2}@{t}-\BesselJ{\nu+1}^{2}@{t}\right)\diff{t} = 2\nu\BesselJ{\nu}^{2}@{x}} | int(t*((BesselJ(nu - 1, t))^(2)- (BesselJ(nu + 1, t))^(2)), t = 0..x) = 2*nu*(BesselJ(nu, x))^(2) |
Integrate[t*((BesselJ[\[Nu]- 1, t])^(2)- (BesselJ[\[Nu]+ 1, t])^(2)), {t, 0, x}, GenerateConditions->None] == 2*\[Nu]*(BesselJ[\[Nu], x])^(2) |
Successful | Successful | - | Successful [Tested: 15] |
| 10.22.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\BesselJ{0}^{2}@{t}\diff{t} = \tfrac{1}{2}x^{2}\left(\BesselJ{0}^{2}@{x}+\BesselJ{1}^{2}@{x}\right)} | int(t*(BesselJ(0, t))^(2), t = 0..x) = (1)/(2)*(x)^(2)*((BesselJ(0, x))^(2)+ (BesselJ(1, x))^(2)) |
Integrate[t*(BesselJ[0, t])^(2), {t, 0, x}, GenerateConditions->None] == Divide[1,2]*(x)^(2)*((BesselJ[0, x])^(2)+ (BesselJ[1, x])^(2)) |
Successful | Successful | - | Successful [Tested: 3] |
| 10.22.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{n}@{t}\BesselJ{n+1}@{t}\diff{t} = \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x}} | int(BesselJ(n, t)*BesselJ(n + 1, t), t = 0..x) = (1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n) |
Integrate[BesselJ[n, t]*BesselJ[n + 1, t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 3] | Failed [2 / 3]
{Plus[-0.6308420033135872, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]], {Rule[n, 3], Rule[x, 1.5]}Plus[-0.9403627636501156, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[0.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[0.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[0.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[0.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[0.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 0.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2], Times[Power[0.5, -2], Power[Plus[Times[-1, 0.5, BesselJ[0, 0.5]], Times[2, BesselJ[1, 0.5]]], 2]]]]}]][4.0]], {Rule[n, 3], Rule[x, 0.5]} |
| 10.22.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x} = \sum_{k=n+1}^{\infty}\BesselJ{k}^{2}@{x}} | (1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n) = sum((BesselJ(k, x))^(2), k = n + 1..infinity) |
Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None] == Sum[(BesselJ[k, x])^(2), {k, n + 1, Infinity}, GenerateConditions->None] |
Failure | Failure | Successful [Tested: 3] | Failed [3 / 3]
{Plus[0.6309837827773054, Times[-1.0, NSum[Power[BesselJ[k, 1.5], 2] <- {k, 4, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]]], {Rule[n, 3], Rule[x, 1.5]}Plus[0.9403627895513045, Times[-1.0, NSum[Power[BesselJ[k, 0.5], 2] <- {k, 4, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], Power[0.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[0.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[0.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[0.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[0.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 0.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2], Times[Power[0.5, -2], Power[Plus[Times[-1, 0.5, BesselJ[0, 0.5]], Times[2, BesselJ[1, 0.5]]], 2]]]]}]][4.0]]], {Rule[n, 3], Rule[x, 0.5]} |
| 10.22.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{\mu+\nu+2k+1}@{x}} | int(BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x) = 2*sum((- 1)^(k)* BesselJ(mu + nu + 2*k + 1, x), k = 0..infinity) |
Integrate[BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == 2*Sum[(- 1)^(k)* BesselJ[\[Mu]+ \[Nu]+ 2*k + 1, x], {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Skip - No test values generated |
| 10.22.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{1-\nu}@{x-t}\diff{t} = \BesselJ{0}@{x}-\cos@@{x}} | int(BesselJ(nu, t)*BesselJ(1 - nu, x - t), t = 0..x) = BesselJ(0, x)- cos(x) |
Integrate[BesselJ[\[Nu], t]*BesselJ[1 - \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == BesselJ[0, x]- Cos[x] |
Failure | Failure | - | Skipped - Because timed out |
| 10.22.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{-\nu}@{x-t}\diff{t} = \sin@@{x}} | int(BesselJ(nu, t)*BesselJ(- nu, x - t), t = 0..x) = sin(x) |
Integrate[BesselJ[\[Nu], t]*BesselJ[- \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Sin[x] |
Failure | Failure | - | Skipped - Because timed out |
| 10.22.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{-1}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = \frac{\BesselJ{\mu+\nu}@{x}}{\mu}} | int((t)^(- 1)* BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x) = (BesselJ(mu + nu, x))/(mu) |
Integrate[(t)^(- 1)* BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Divide[BesselJ[\[Mu]+ \[Nu], x],\[Mu]] |
Failure | Failure | - | Skip - No test values generated |
| 10.22.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t}}{t(x-t)} = \frac{(\mu+\nu)\BesselJ{\mu+\nu}@{x}}{\mu\nu x}} | int((BesselJ(mu, t)*BesselJ(nu, x - t))/(t*(x - t)), t = 0..x) = ((mu + nu)* BesselJ(mu + nu, x))/(mu*nu*x) |
Integrate[Divide[BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t],t*(x - t)], {t, 0, x}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu])* BesselJ[\[Mu]+ \[Nu], x],\[Mu]*\[Nu]*x] |
Error | Failure | - | Skip - No test values generated |
| 10.22.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{\alpha}}\int_{0}^{x}(x-t)^{\alpha-1}\BesselJ{\nu}@{t}\diff{t} = 2^{\alpha}\sum_{k=0}^{\infty}\frac{(\alpha)_{k}}{k!}\BesselJ{\nu+\alpha+2k}@{x}} | (1)/(GAMMA(alpha))*int((x - t)^(alpha - 1)* BesselJ(nu, t), t = 0..x) = (2)^(alpha)* sum((alpha[k])/(factorial(k))*BesselJ(nu + alpha + 2*k, x), k = 0..infinity) |
Divide[1,Gamma[\[Alpha]]]*Integrate[(x - t)^(\[Alpha]- 1)* BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == (2)^\[Alpha]* Sum[Divide[Subscript[\[Alpha], k],(k)!]*BesselJ[\[Nu]+ \[Alpha]+ 2*k, x], {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Skip - No test values generated |
| 10.22.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t\BesselJ{\nu}@{j_{\nu,\ell}t}\BesselJ{\nu}@{j_{\nu,m}t}\diff{t} = \tfrac{1}{2}\left(\BesselJ{\nu}'@{j_{\nu,\ell}}\right)^{2}\Kroneckerdelta{\ell}{m}} | int(t*BesselJ(nu, j[nu , ell]*t)*BesselJ(nu, j[nu , m]*t), t = 0..1) = (1)/(2)*(diff( BesselJ(nu, j[nu , ell]), j[nu , ell]$(1) ))^(2)* KroneckerDelta[ell, m] |
Integrate[t*BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[j, \[Nu], m]*t], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(D[BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]], {Subscript[j, \[Nu], \[ScriptL]], 1}])^(2)* KroneckerDelta[\[ScriptL], m] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[m, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[m, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.22.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t\BesselJ{\nu}@{\alpha_{\ell}t}\BesselJ{\nu}@{\alpha_{m}t}\diff{t} = \left(\frac{a^{2}}{b^{2}}+\alpha_{\ell}^{2}-\nu^{2}\right)\frac{(\BesselJ{\nu}@{\alpha_{\ell}})^{2}}{2\alpha_{\ell}^{2}}\Kroneckerdelta{\ell}{m}} | int(t*BesselJ(nu, alpha[ell]*t)*BesselJ(nu, alpha[m]*t), t = 0..1) ((BesselJ(nu, alpha[ell]))^(2))/(2*alpha(alpha[ell])^(2))*KroneckerDelta[ell, m] |
Integrate[t*BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[\[Alpha], m]*t], {t, 0, 1}, GenerateConditions->None] Divide[(BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]])^(2),2*\[Alpha](Subscript[\[Alpha], \[ScriptL]])^(2)]*KroneckerDelta[\[ScriptL], m] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[m, 1], Rule[α, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[m, 2], Rule[α, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.22.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\BesselJ{0}@{t}}{t}\diff{t}+\EulerConstant+\ln@{\tfrac{1}{2}x} = \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t}} | int((BesselJ(0, t))/(t), t = x..infinity)+ gamma + ln((1)/(2)*x) = int((1 - BesselJ(0, t))/(t), t = 0..x) |
Integrate[Divide[BesselJ[0, t],t], {t, x, Infinity}, GenerateConditions->None]+ EulerGamma + Log[Divide[1,2]*x] == Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 3] |
| 10.22.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \sum_{k=1}^{\infty}(-1)^{k-1}\frac{(\frac{1}{2}x)^{2k}}{2k(k!)^{2}}} | int((1 - BesselJ(0, t))/(t), t = 0..x) = sum((- 1)^(k - 1)*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity) |
Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Sum[(- 1)^(k - 1)*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 3] |
| 10.22.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{t}\diff{t} = 1} | int(BesselJ(nu, t), t = 0..infinity) = 1 |
Integrate[BesselJ[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == 1 |
Successful | Successful | - | Successful [Tested: 8] |
| 10.22.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{\nu}@{t}\diff{t} = -\tan@{\tfrac{1}{2}\nu\pi}} | int(BesselY(nu, t), t = 0..infinity) = - tan((1)/(2)*nu*Pi) |
Integrate[BesselY[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == - Tan[Divide[1,2]*\[Nu]*Pi] |
Successful | Error | - | Successful [Tested: 6] |
| 10.22.E43 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = 2^{\mu}\frac{\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+\tfrac{1}{2}}}} | int((t)^(mu)* BesselJ(nu, t), t = 0..infinity) = (2)^(mu)*(GAMMA((1)/(2)*nu +(1)/(2)*mu +(1)/(2)))/(GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2))) |
Integrate[(t)^\[Mu]* BesselJ[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == (2)^\[Mu]*Divide[Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[1,2]],Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]] |
Successful | Successful | - | Successful [Tested: 10] |
| 10.22.E55 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{-1}\BesselJ{\nu+2\ell+1}@{t}\BesselJ{\nu+2m+1}@{t}\diff{t} = \frac{\Kroneckerdelta{\ell}{m}}{2(2\ell+\nu+1)}} | int((t)^(- 1)* BesselJ(nu + 2*ell + 1, t)*BesselJ(nu + 2*m + 1, t), t = 0..infinity) = (KroneckerDelta[ell, m])/(2*(2*ell + nu + 1)) |
Integrate[(t)^(- 1)* BesselJ[\[Nu]+ 2*\[ScriptL]+ 1, t]*BesselJ[\[Nu]+ 2*m + 1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[KroneckerDelta[\[ScriptL], m],2*(2*\[ScriptL]+ \[Nu]+ 1)] |
Failure | Failure | Error | Failed [30 / 30]
{Plus[Times[-0.5, Power[Plus[Complex[1.8660254037844388, 0.49999999999999994], Times[2.0, ℓ]], -1], KroneckerDelta[1.0, ℓ]], Times[0.15915494309189535, Power[Plus[1.0, Times[-1.0, ℓ]], -1], Power[Plus[Complex[2.866025403784439, 0.49999999999999994], ℓ], -1], Sin[Times[3.141592653589793, Plus[1.0, Times[-1.0, ℓ]]]]]] <- {Rule[m, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Times[-0.5, Power[Plus[Complex[1.8660254037844388, 0.49999999999999994], Times[2.0, ℓ]], -1], KroneckerDelta[2.0, ℓ]], Times[0.15915494309189535, Power[Plus[2.0, Times[-1.0, ℓ]], -1], Power[Plus[Complex[3.866025403784439, 0.49999999999999994], ℓ], -1], Sin[Times[3.141592653589793, Plus[2.0, Times[-1.0, ℓ]]]]]] <- {Rule[m, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.23.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}^{2}@{z}+2\sum_{k=1}^{\infty}\BesselJ{k}^{2}@{z} = 1} | (BesselJ(0, z))^(2)+ 2*sum((BesselJ(k, z))^(2), k = 1..infinity) = 1 |
(BesselJ[0, z])^(2)+ 2*Sum[(BesselJ[k, z])^(2), {k, 1, Infinity}, GenerateConditions->None] == 1 |
Error | Successful | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{2n}(-1)^{k}\BesselJ{k}@{z}\BesselJ{2n-k}@{z}\\ +2\sum_{k=1}^{\infty}\BesselJ{k}@{z}\BesselJ{2n+k}@{z} = 0} | sum((- 1)^(k)* BesselJ(k, z)*BesselJ(2*n - k, z), k = 0..2*n)+ 2*sum(BesselJ(k, z)*BesselJ(2*n + k, z), k = 1..infinity) = 0 |
Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[2*n - k, z], {k, 0, 2*n}, GenerateConditions->None]+ 2*Sum[BesselJ[k, z]*BesselJ[2*n + k, z], {k, 1, Infinity}, GenerateConditions->None] == 0 |
Error | Failure | - | Failed [21 / 21]
{Plus[Complex[0.00727987412712798, -0.017853077134921347], Times[2.0, NSum[Times[BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[2.4034761502300195*^-4, -3.087748713313073*^-5], Times[2.0, NSum[Times[BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[4, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{n}\BesselJ{k}@{z}\BesselJ{n-k}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{k}@{z}\BesselJ{n+k}@{z} = \BesselJ{n}@{2z}} | sum(BesselJ(k, z)*BesselJ(n - k, z), k = 0..n)+ 2*sum((- 1)^(k)* BesselJ(k, z)*BesselJ(n + k, z), k = 1..infinity) = BesselJ(n, 2*z) |
Sum[BesselJ[k, z]*BesselJ[n - k, z], {k, 0, n}, GenerateConditions->None]+ 2*Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[n + k, z], {k, 1, Infinity}, GenerateConditions->None] == BesselJ[n, 2*z] |
Error | Failure | Skipped - Because timed out | Failed [21 / 21]
{Plus[Complex[0.024343533040476317, 0.10797471990649704], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[1, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.006069425709337772, 0.017711723121060452], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.23#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \sqrt{u^{2}+v^{2}-2uv\cos@@{\alpha}}} | w = sqrt((u)^(2)+ (v)^(2)- 2*u*v*cos(alpha)) |
w == Sqrt[(u)^(2)+ (v)^(2)- 2*u*v*Cos[\[Alpha]]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.3146075610-.1816387601*I <- {alpha = 3/2, u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I}-1.680632965+.1843866439*I <- {alpha = 3/2, u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-0.3146075609842255, -0.18163876002333418] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Complex[0.4375091763619045, 0.252596040745477] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.23#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u-v\cos@@{\alpha} = w\cos@@{\chi}} | u - v*cos(alpha) = w*cos(chi) |
u - v*Cos[\[Alpha]] == w*Cos[\[Chi]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.263783978e-1+.4431282844*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I}.8262683052-.3665121890*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-0.026378398027867456, 0.44312828415668515] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.023973249213014358, -0.5554825514041751] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.23#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v\sin@@{\alpha} = w\sin@@{\chi}} | v*sin(alpha) = w*sin(chi) |
v*Sin[\[Alpha]] == w*Sin[\[Chi]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.2887554391-.2231097873*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I}1.585713279-.763530664e-1*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2)} |
Failed [294 / 300]
{Complex[0.2887554393029954, -0.22310978722682606] <- {Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.8740447527972026, 0.09051196331992012] <- {Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.23.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{iv\cos@@{\alpha}} = \frac{\EulerGamma@{\nu}}{(\tfrac{1}{2}v)^{\nu}}\*\sum_{k=0}^{\infty}(\nu+k)i^{k}\BesselJ{\nu+k}@{v}\ultrasphpoly{\nu}{k}@{\cos@@{\alpha}}} | exp(I*v*cos(alpha)) = (GAMMA(nu))/(((1)/(2)*v)^(nu))* sum((nu + k)* (I)^(k)* BesselJ(nu + k, v)*GegenbauerC(k, nu, cos(alpha)), k = 0..infinity) |
Exp[I*v*Cos[\[Alpha]]] == Divide[Gamma[\[Nu]],(Divide[1,2]*v)^\[Nu]]* Sum[(\[Nu]+ k)* (I)^(k)* BesselJ[\[Nu]+ k, v]*GegenbauerC[k, \[Nu], Cos[\[Alpha]]], {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 10.23.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}z)^{\nu} = \sum_{k=0}^{\infty}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\BesselJ{\nu+2k}@{z}} | ((1)/(2)*z)^(nu) = sum(((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselJ(nu + 2*k, z), k = 0..infinity) |
(Divide[1,2]*z)^\[Nu] == Sum[Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselJ[\[Nu]+ 2*k, z], {k, 0, Infinity}, GenerateConditions->None] |
Error | Successful | Skipped - Because timed out | Successful [Tested: 7] |
| 10.23.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}-\frac{4}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{\BesselJ{2k}@{z}}{k}} | BesselY(0, z) = (2)/(Pi)*(ln((1)/(2)*z)+ gamma)* BesselJ(0, z)-(4)/(Pi)*sum((- 1)^(k)*(BesselJ(2*k, z))/(k), k = 1..infinity) |
BesselY[0, z] == Divide[2,Pi]*(Log[Divide[1,2]*z]+ EulerGamma)* BesselJ[0, z]-Divide[4,Pi]*Sum[(- 1)^(k)*Divide[BesselJ[2*k, z],k], {k, 1, Infinity}, GenerateConditions->None] |
Error | Successful | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.23.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{z} = -\frac{n!(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}\BesselJ{k}@{z}}{k!(n-k)}+\frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\BesselJ{n}@{z}-\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{(n+2k)\BesselJ{n+2k}@{z}}{k(n+k)}} | BesselY(n, z) = -(factorial(n)*((1)/(2)*z)^(- n))/(Pi)*sum((((1)/(2)*z)^(k)* BesselJ(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(2)/(Pi)*(ln((1)/(2)*z)- Psi(n + 1))* BesselJ(n, z)-(2)/(Pi)*sum((- 1)^(k)*((n + 2*k)* BesselJ(n + 2*k, z))/(k*(n + k)), k = 1..infinity) |
BesselY[n, z] == -Divide[(n)!*(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(Divide[1,2]*z)^(k)* BesselJ[k, z],(k)!*(n - k)], {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselJ[n, z]-Divide[2,Pi]*Sum[(- 1)^(k)*Divide[(n + 2*k)* BesselJ[n + 2*k, z],k*(n + k)], {k, 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [16 / 21]
{Plus[Complex[-0.41373222494160333, 0.38808044477324316], Times[Complex[0.5513288954217921, -0.31830988618379064], DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[Times[-1, ], 1], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], []], Times[Plus[4, Times[12, ], Times[12, Power[, 2]], Times[4, Power[, 3]], Times[-4, 1], Times[-8, , 1], Times[-4, Power[, 2], 1], Times[, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-1, 1, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], [Plus[1, ]]], Times[4, Plus[1, ], Plus[-5, Times[-6, ], Times[-2, Power[, 2]], Times[3, 1], Times[2, , 1]], [Plus[2, ]]], Times[-4, Plus[1, ], Plus[2, ], Plus[-2, Times[-1, ], 1], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[1, 2], Power[Plus[-1, 1], -1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], BesselJ[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.6198631863998064, 5.383408526303685], Times[Complex[0.0, -15.278874536821952], DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-1, Power[-1, Rational[1, 3]], Plus[-3, ], []], Times[Plus[-8, Times[-3, Power[-1, Rational[1, 3]]], Times[-12, ], Times[Power[-1, Rational[1, 3]], ], Times[4, Power[, 3]]], [Plus[1, ]]], Times[-8, Plus[1, ], Plus[-2, Power[, 2]], [Plus[2, ]]], Times[4, Plus[-1, ], Plus[1, ], Plus[2, ], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Rational[1, 3], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Rational[1, 3], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[1, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], BesselJ[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][3.0]]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(x^{2}+\nu^{2})w = 0} | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((x)^(2)+ (nu)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+((x)^(2)+ \[Nu]^(2))* w == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.948557159+2.125000000*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}.2165063513+1.125000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[1.9485571585149875, 2.125] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.948557158514987, 0.12499999999999989] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.24#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJimag{\nu}@{x} = \sech@{\tfrac{1}{2}\pi\nu}\realpart@{\BesselJ{i\nu}@{x}}} | sech((1/2)*Pi*(nu))*Re(BesselJ(I*(nu), x)) = sech((1)/(2)*Pi*nu)*Re(BesselJ(I*nu, x)) |
Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]] == Sech[Divide[1,2]*Pi*\[Nu]]*Re[BesselJ[I*\[Nu], x]] |
Successful | Successful | - | Successful [Tested: 30] |
| 10.24#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{\nu}@{x} = \sech@{\tfrac{1}{2}\pi\nu}\realpart@{\BesselY{i\nu}@{x}}} | sech((1/2)*Pi*(nu))*Re(BesselY(I*(nu), x)) = sech((1)/(2)*Pi*nu)*Re(BesselY(I*nu, x)) |
Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]] == Sech[Divide[1,2]*Pi*\[Nu]]*Re[BesselY[I*\[Nu], x]] |
Successful | Successful | - | Successful [Tested: 30] |
| 10.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{1+i\nu} = \left(\frac{\pi\nu}{\sinh@{\pi\nu}}\right)^{\frac{1}{2}}e^{i\gamma_{\nu}}} | GAMMA(1 + I*nu) = ((Pi*nu)/(sinh(Pi*nu)))^((1)/(2))* exp(I*gamma[nu]) |
Gamma[1 + I*\[Nu]] == (Divide[Pi*\[Nu],Sinh[Pi*\[Nu]]])^(Divide[1,2])* Exp[I*Subscript[\[Gamma], \[Nu]]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.131682196e-1-.6479738907*I <- {gamma = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, gamma[nu] = 1/2*3^(1/2)+1/2*I}.2393622021-.2867640040*I <- {gamma = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, gamma[nu] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.013168219691258531, -0.6479738909120968] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.23936220222535412, -0.28676400411697583] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, ν], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.24#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJimag{-\nu}@{x} = \BesselJimag{\nu}@{x}} | sech((1/2)*Pi*(- nu))*Re(BesselJ(I*(- nu), x)) = sech((1/2)*Pi*(nu))*Re(BesselJ(I*(nu), x)) |
Sech[1/2 Pi - \[Nu]] Re[BesselJ[I - \[Nu], x]] == Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]] |
Failure | Failure | Failed [12 / 30] 12/30]: [[.1765981285-.1547836875*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}-1.059084556+.9282601935*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [30 / 30]
{Complex[-0.6353785354467336, 0.04153700144653363] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.2910880978413849, 0.681683596996288] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.24#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{-\nu}@{x} = \BesselYimag{\nu}@{x}} | sech((1/2)*Pi*(- nu))*Re(BesselY(I*(- nu), x)) = sech((1/2)*Pi*(nu))*Re(BesselY(I*(nu), x)) |
Sech[1/2 Pi - \[Nu]] Re[BesselY[I - \[Nu], x]] == Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]] |
Failure | Failure | Failed [12 / 30] 12/30]: [[-.6730010946+.5898680353*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}-.1980888923+.1736197856*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [30 / 30]
{Complex[0.16541121369118172, 0.7534126929509344] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.3242468905843751, -0.9796849117084342] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.24.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJimag{\nu}@{x},\BesselYimag{\nu}@{x}} = 2/(\pi x)} | (sech((1/2)*Pi*(nu))*Re(BesselJ(I*(nu), x)))*diff(sech((1/2)*Pi*(nu))*Re(BesselY(I*(nu), x)), x)-diff(sech((1/2)*Pi*(nu))*Re(BesselJ(I*(nu), x)), x)*(sech((1/2)*Pi*(nu))*Re(BesselY(I*(nu), x))) = 2/(Pi*x) |
Wronskian[{Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]], Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]]}, x] == 2/(Pi*x) |
Failure | Failure | Failed [12 / 30] 12/30]: [[-.3214564733-.7786157192*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}-.6431025084-4.765445687*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [30 / 30]
{Plus[-0.4244131815783876, Times[Complex[0.017184424665049866, -0.12995814793225188], Plus[Times[Complex[5.94457417937745, -0.08806734388290616], Derivative[1][Re][Complex[0.5424102683642863, 1.3820413572565333]]], Times[Complex[0.04670634387761448, 2.0064149502593187], Derivative[1][Re][Complex[1.5013396639532606, -0.5145465005058608]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[-0.4244131815783876, Times[Complex[-0.5062208144169521, 0.3689208146583662], Plus[Times[Complex[1.2690034139339206, -1.428145592425075], Derivative[1][Re][Complex[-0.5230512553281585, -0.7250724679588263]]], Times[Complex[0.9907135967899046, 0.5862869255257461], Derivative[1][Re][Complex[0.9118063408652576, -0.381897212811936]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{0}@{x} = \BesselY{0}@{x}} | sech((1/2)*Pi*(0))*Re(BesselY(I*(0), x)) = BesselY(0, x) |
Sech[1/2 Pi 0] Re[BesselY[I 0, x]] == BesselY[0, x] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.25.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0} | (z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)-((z)^(2)+ (nu)^(2))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ z*D[w, z]-((z)^(2)+ \[Nu]^(2))* w == 0 |
Failure | Failure | Failed [220 / 300] 220/300]: [[-.6467477718e-9-2.000000002*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-.8660254040e-9-2.000000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I} |
Failed [264 / 300]
{Complex[0.0, -2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.0, -2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} |
| 10.25.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}} | BesselI(nu, z) = ((1)/(2)*z)^(nu)* sum((((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity) |
BesselI[\[Nu], z] == (Divide[1,2]*z)^\[Nu]* Sum[Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.27.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-n}@{z} = \modBesselI{n}@{z}} | BesselI(- n, z) = BesselI(n, z) |
BesselI[- n, z] == BesselI[n, z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.27.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z}} | BesselI(- nu, z) = BesselI(nu, z)+(2/ Pi)* sin(nu*Pi)*BesselK(nu, z) |
BesselI[- \[Nu], z] == BesselI[\[Nu], z]+(2/ Pi)* Sin[\[Nu]*Pi]*BesselK[\[Nu], z] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.27.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z}} | BesselK(- nu, z) = BesselK(nu, z) |
BesselK[- \[Nu], z] == BesselK[\[Nu], z] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.27.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}}} | BesselK(nu, z) = (1)/(2)*Pi*(BesselI(- nu, z)- BesselI(nu, z))/(sin(nu*Pi)) |
BesselK[\[Nu], z] == Divide[1,2]*Pi*Divide[BesselI[- \[Nu], z]- BesselI[\[Nu], z],Sin[\[Nu]*Pi]] |
Successful | Successful | - | Failed [14 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]} |
| 10.27.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}}} | BesselI(nu, z) = exp(- nu*Pi*I/ 2)*BesselJ(nu, z*exp(+ Pi*I/ 2)) |
BesselI[\[Nu], z] == Exp[- \[Nu]*Pi*I/ 2]*BesselJ[\[Nu], z*Exp[+ Pi*I/ 2]] |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}}} | BesselI(nu, z) = exp(+ nu*Pi*I/ 2)*BesselJ(nu, z*exp(- Pi*I/ 2)) |
BesselI[\[Nu], z] == Exp[+ \[Nu]*Pi*I/ 2]*BesselJ[\[Nu], z*Exp[- Pi*I/ 2]] |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right)} | BesselI(nu, z) = (1)/(2)*exp(- nu*Pi*I/ 2)*(HankelH1(nu, z*exp(+ Pi*I/ 2))+ HankelH2(nu, z*exp(+ Pi*I/ 2))) |
BesselI[\[Nu], z] == Divide[1,2]*Exp[- \[Nu]*Pi*I/ 2]*(HankelH1[\[Nu], z*Exp[+ Pi*I/ 2]]+ HankelH2[\[Nu], z*Exp[+ Pi*I/ 2]]) |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right)} | BesselI(nu, z) = (1)/(2)*exp(+ nu*Pi*I/ 2)*(HankelH1(nu, z*exp(- Pi*I/ 2))+ HankelH2(nu, z*exp(- Pi*I/ 2))) |
BesselI[\[Nu], z] == Divide[1,2]*Exp[+ \[Nu]*Pi*I/ 2]*(HankelH1[\[Nu], z*Exp[- Pi*I/ 2]]+ HankelH2[\[Nu], z*Exp[- Pi*I/ 2]]) |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}} | Pi*I*BesselJ(nu, z) = exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2))- exp(nu*Pi*I/ 2)*BesselK(nu, z*exp(Pi*I/ 2)) |
Pi*I*BesselJ[\[Nu], z] == Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]]- Exp[\[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[Pi*I/ 2]] |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}} | - Pi*BesselY(nu, z) = exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2))+ exp(nu*Pi*I/ 2)*BesselK(nu, z*exp(Pi*I/ 2)) |
- Pi*BesselY[\[Nu], z] == Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]]+ Exp[\[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[Pi*I/ 2]] |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}} | BesselY(nu, z) = exp(+(nu + 1)* Pi*I/ 2)*BesselI(nu, z*exp(- Pi*I/ 2))-(2/ Pi)* exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2)) |
BesselY[\[Nu], z] == Exp[+(\[Nu]+ 1)* Pi*I/ 2]*BesselI[\[Nu], z*Exp[- Pi*I/ 2]]-(2/ Pi)* Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]] |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.27.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}}} | BesselY(nu, z) = exp(-(nu + 1)* Pi*I/ 2)*BesselI(nu, z*exp(+ Pi*I/ 2))-(2/ Pi)* exp(+ nu*Pi*I/ 2)*BesselK(nu, z*exp(+ Pi*I/ 2)) |
BesselY[\[Nu], z] == Exp[-(\[Nu]+ 1)* Pi*I/ 2]*BesselI[\[Nu], z*Exp[+ Pi*I/ 2]]-(2/ Pi)* Exp[+ \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[+ Pi*I/ 2]] |
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
| 10.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselI{\nu}@{z},\modBesselI{-\nu}@{z}} = \modBesselI{\nu}@{z}\modBesselI{-\nu-1}@{z}-\modBesselI{\nu+1}@{z}\modBesselI{-\nu}@{z}} | (BesselI(nu, z))*diff(BesselI(- nu, z), z)-diff(BesselI(nu, z), z)*(BesselI(- nu, z)) = BesselI(nu, z)*BesselI(- nu - 1, z)- BesselI(nu + 1, z)*BesselI(- nu, z) |
Wronskian[{BesselI[\[Nu], z], BesselI[- \[Nu], z]}, z] == BesselI[\[Nu], z]*BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]*BesselI[- \[Nu], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselI{-\nu-1}@{z}-\modBesselI{\nu+1}@{z}\modBesselI{-\nu}@{z} = -2\sin@{\nu\pi}/(\pi z)} | BesselI(nu, z)*BesselI(- nu - 1, z)- BesselI(nu + 1, z)*BesselI(- nu, z) = - 2*sin(nu*Pi)/(Pi*z) |
BesselI[\[Nu], z]*BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]*BesselI[- \[Nu], z] == - 2*Sin[\[Nu]*Pi]/(Pi*z) |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselK{\nu}@{z},\modBesselI{\nu}@{z}} = \modBesselI{\nu}@{z}\modBesselK{\nu+1}@{z}+\modBesselI{\nu+1}@{z}\modBesselK{\nu}@{z}} | (BesselK(nu, z))*diff(BesselI(nu, z), z)-diff(BesselK(nu, z), z)*(BesselI(nu, z)) = BesselI(nu, z)*BesselK(nu + 1, z)+ BesselI(nu + 1, z)*BesselK(nu, z) |
Wronskian[{BesselK[\[Nu], z], BesselI[\[Nu], z]}, z] == BesselI[\[Nu], z]*BesselK[\[Nu]+ 1, z]+ BesselI[\[Nu]+ 1, z]*BesselK[\[Nu], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 70] |
| 10.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselK{\nu+1}@{z}+\modBesselI{\nu+1}@{z}\modBesselK{\nu}@{z} = 1/z} | BesselI(nu, z)*BesselK(nu + 1, z)+ BesselI(nu + 1, z)*BesselK(nu, z) = 1/ z |
BesselI[\[Nu], z]*BesselK[\[Nu]+ 1, z]+ BesselI[\[Nu]+ 1, z]*BesselK[\[Nu], z] == 1/ z |
Failure | Successful | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.29#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}'@{z} = \modBesselI{1}@{z}} | diff( BesselI(0, z), z$(1) ) = BesselI(1, z) |
D[BesselI[0, z], {z, 1}] == BesselI[1, z] |
Successful | Successful | - | Successful [Tested: 7] |
| 10.29#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}'@{z} = -\modBesselK{1}@{z}} | diff( BesselK(0, z), z$(1) ) = - BesselK(1, z) |
D[BesselK[0, z], {z, 1}] == - BesselK[1, z] |
Successful | Successful | - | Successful [Tested: 7] |
| 10.31.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\modBesselI{0}@{z}+\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}+(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}+\dotsi} | BesselK(0, z) = -(ln((1)/(2)*z)+ gamma)* BesselI(0, z)+((1)/(4)*(z)^(2))/((factorial(1))^(2))+(1 +(1)/(2))*(((1)/(4)*(z)^(2))^(2))/((factorial(2))^(2))+(1 +(1)/(2)+(1)/(3))*(((1)/(4)*(z)^(2))^(3))/((factorial(3))^(2))+ .. |
BesselK[0, z] == -(Log[Divide[1,2]*z]+ EulerGamma)* BesselI[0, z]+Divide[Divide[1,4]*(z)^(2),((1)!)^(2)]+(1 +Divide[1,2])*Divide[(Divide[1,4]*(z)^(2))^(2),((2)!)^(2)]+(1 +Divide[1,2]+Divide[1,3])*Divide[(Divide[1,4]*(z)^(2))^(3),((3)!)^(2)]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-6.985673039111573*^-6, -1.2369744460005716*^-5], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-7.140527721077872*^-6, -1.2101549865001227*^-5], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.31.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselI{\mu}@{z} = (\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}\EulerGamma@{\mu+k+1}}} | BesselI(nu, z)*BesselI(mu, z) = ((1)/(2)*z)^(nu + mu)* sum((nu + mu + k + 1[k]*((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)*GAMMA(mu + k + 1)), k = 0..infinity) |
BesselI[\[Nu], z]*BesselI[\[Mu], z] == (Divide[1,2]*z)^(\[Nu]+ \[Mu])* Sum[Divide[Subscript[\[Nu]+ \[Mu]+ k + 1, k]*(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]*Gamma[\[Mu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}} | BesselI(0, z) = (1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi) |
BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}} | BesselI(0, z) = (1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi) |
BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}} | (1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Successful [Tested: 7] |
| 10.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}} | (1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi) |
Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Successful [Tested: 7] |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) |
BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Successful [Tested: 35] |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}} | BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) |
BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Successful [Tested: 35] |
| 10.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}} | (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(+ z*t), t = - 1..1) |
Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Successful [Tested: 35] |
| 10.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}} | BesselI(n, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(n*theta), theta = 0..Pi) |
BesselI[n, z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 21] | Skipped - Because timed out |
| 10.32.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}} | BesselI(nu, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity) |
BesselI[\[Nu], z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[\[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Cosh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.32.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}} | BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity) |
BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] |
Successful | Error | - | Skipped - Because timed out |
| 10.32.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}} | int(cos(x*sinh(t)), t = 0..infinity) = int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity) |
Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[x*t],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None] |
Successful | Error | - | Skipped - Because timed out |
| 10.32.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}} | BesselK(nu, x) = sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) |
BesselK[\[Nu], x] == Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Successful | Error | - | Skipped - Because timed out |
| 10.32.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}} | sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) = csc((1)/(2)*nu*Pi)*int(sin(x*sinh(t))*sinh(nu*t), t = 0..infinity) |
Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]*\[Nu]*Pi]*Integrate[Sin[x*Sinh[t]]*Sinh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | - | Skipped - Because timed out |
| 10.32.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}} | BesselK(nu, z) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity) |
BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.32.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}} | BesselK(nu, z) = int(exp(- z*cosh(t))*cosh(nu*t), t = 0..infinity) |
BesselK[\[Nu], z] == Integrate[Exp[- z*Cosh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.32.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}} | BesselK(nu, z) = (1)/(2)*((1)/(2)*z)^(nu)* int(exp(- t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = 0..infinity) |
BesselK[\[Nu], z] == Divide[1,2]*(Divide[1,2]*z)^\[Nu]* Integrate[Exp[- t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 40] |
| 10.32.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}} | BesselI(nu, z) = (1)/(2*Pi*I)*int(exp(z*cosh(t)- nu*t), t = infinity - I*Pi..infinity + I*Pi) |
BesselI[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Cosh[t]- \[Nu]*t], {t, Infinity - I*Pi, Infinity + I*Pi}, GenerateConditions->None] |
Error | Failure | - | Failed [50 / 50]
{Complex[0.5303418993681409, 0.010453999760907294] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.7664848208906112, 0.1468422559210476] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.32.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}} | BesselK(nu, z) = (((1)/(2)*z)^(nu))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity) |
BesselK[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],4*Pi*I]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] |
Failure | Error | Failed [300 / 300] 300/300]: [[.5663982443-.3181066824*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}-1.434992817-2.759712160*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 10.32.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}} | BesselK(nu, z) = (1)/(2*(Pi)^(2)* I)*((Pi)/(2*z))^((1)/(2))* exp(- z)*cos(nu*Pi)* int(GAMMA(t)*GAMMA((1)/(2)- t - nu)*GAMMA((1)/(2)- t + nu)*(2*z)^(t), t = - I*infinity..I*infinity) |
BesselK[\[Nu], z] == Divide[1,2*(Pi)^(2)* I]*(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*Cos[\[Nu]*Pi]* Integrate[Gamma[t]*Gamma[Divide[1,2]- t - \[Nu]]*Gamma[Divide[1,2]- t + \[Nu]]*(2*z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.32.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}} | BesselI(mu, z)*BesselI(nu, z) = (2)/(Pi)*int(BesselI(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..(1)/(2)*Pi) |
BesselI[\[Mu], z]*BesselI[\[Nu], z] == Divide[2,Pi]*Integrate[BesselI[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.32.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}} | BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)* t), t = 0..infinity) |
BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]- \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | - | Skipped - Because timed out |
| 10.32.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}} | BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)* t), t = 0..infinity) |
BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]+ \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None] |
Failure | Error | - | Skipped - Because timed out |
| 10.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\modBesselI{\nu}@{z}} | BesselI(nu, z*exp(m*Pi*I)) = exp(m*nu*Pi*I)*BesselI(nu, z) |
BesselI[\[Nu], z*Exp[m*Pi*I]] == Exp[m*\[Nu]*Pi*I]*BesselI[\[Nu], z] |
Failure | Failure | Failed [132 / 210] 132/210]: [[-2.206479866-1.131319388*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.5147384726+.2724622562e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [120 / 210]
{Complex[-2.206479866313521, -1.1313193889480602] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5147384728800724, 0.02724622519878004] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\modBesselK{\nu}@{z}-\pi i\sin@{m\nu\pi}\csc@{\nu\pi}\modBesselI{\nu}@{z}} | BesselK(nu, z*exp(m*Pi*I)) = exp(- m*nu*Pi*I)*BesselK(nu, z)- Pi*I*sin(m*nu*Pi)*csc(nu*Pi)*BesselI(nu, z) |
BesselK[\[Nu], z*Exp[m*Pi*I]] == Exp[- m*\[Nu]*Pi*I]*BesselK[\[Nu], z]- Pi*I*Sin[m*\[Nu]*Pi]*Csc[\[Nu]*Pi]*BesselI[\[Nu], z] |
Failure | Failure | Failed [170 / 210] 170/210]: [[2.965939338+3.157233720*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}-10.37113928-12.75980866*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [162 / 210]
{Complex[2.965939340334436, 3.157233721966529] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-10.371139260352992, -12.75980869099896] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = (i/\pi)\left(+ e^{m\nu\pi i}\modBesselK{\nu}@{ze^{+\pi i}}- e^{(m- 1)\nu\pi i}\modBesselK{\nu}@{z}\right)} | BesselI(nu, z*exp(m*Pi*I)) = (I/ Pi)*(+ exp(m*nu*Pi*I)*BesselK(nu, z*exp(+ Pi*I))- exp((m - 1)* nu*Pi*I)*BesselK(nu, z)) |
BesselI[\[Nu], z*Exp[m*Pi*I]] == (I/ Pi)*(+ Exp[m*\[Nu]*Pi*I]*BesselK[\[Nu], z*Exp[+ Pi*I]]- Exp[(m - 1)* \[Nu]*Pi*I]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [152 / 210] 152/210]: [[-2.316975457-.8668337446*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.5132395470-.3232131754e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [140 / 210]
{Complex[-2.3169754573845194, -0.8668337451474188] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5132395471581521, -0.03232131806579792] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = (i/\pi)\left(- e^{m\nu\pi i}\modBesselK{\nu}@{ze^{-\pi i}}+ e^{(m+ 1)\nu\pi i}\modBesselK{\nu}@{z}\right)} | BesselI(nu, z*exp(m*Pi*I)) = (I/ Pi)*(- exp(m*nu*Pi*I)*BesselK(nu, z*exp(- Pi*I))+ exp((m + 1)* nu*Pi*I)*BesselK(nu, z)) |
BesselI[\[Nu], z*Exp[m*Pi*I]] == (I/ Pi)*(- Exp[m*\[Nu]*Pi*I]*BesselK[\[Nu], z*Exp[- Pi*I]]+ Exp[(m + 1)* \[Nu]*Pi*I]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [190 / 210] 190/210]: [[-2.206479866-1.131319388*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.5147384726+.2724622561e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [190 / 210]
{Complex[-2.206479866313521, -1.1313193889480602] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5147384728800724, 0.027246225198780036] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = \csc@{\nu\pi}\left(+\sin@{m\nu\pi}\modBesselK{\nu}@{ze^{+\pi i}}-\sin@{(m- 1)\nu\pi}\modBesselK{\nu}@{z}\right)} | BesselK(nu, z*exp(m*Pi*I)) = csc(nu*Pi)*(+ sin(m*nu*Pi)*BesselK(nu, z*exp(+ Pi*I))- sin((m - 1)* nu*Pi)*BesselK(nu, z)) |
BesselK[\[Nu], z*Exp[m*Pi*I]] == Csc[\[Nu]*Pi]*(+ Sin[m*\[Nu]*Pi]*BesselK[\[Nu], z*Exp[+ Pi*I]]- Sin[(m - 1)* \[Nu]*Pi]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [158 / 210] 158/210]: [[-2.723238516+7.278993081*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}29.12762958-25.06220737*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 3} |
Failed [154 / 210]
{Complex[-2.7232385256388585, 7.278993075467058] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[29.127629620508102, -25.062207299552764] <- {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = \csc@{\nu\pi}\left(-\sin@{m\nu\pi}\modBesselK{\nu}@{ze^{-\pi i}}+\sin@{(m+ 1)\nu\pi}\modBesselK{\nu}@{z}\right)} | BesselK(nu, z*exp(m*Pi*I)) = csc(nu*Pi)*(- sin(m*nu*Pi)*BesselK(nu, z*exp(- Pi*I))+ sin((m + 1)* nu*Pi)*BesselK(nu, z)) |
BesselK[\[Nu], z*Exp[m*Pi*I]] == Csc[\[Nu]*Pi]*(- Sin[m*\[Nu]*Pi]*BesselK[\[Nu], z*Exp[- Pi*I]]+ Sin[(m + 1)* \[Nu]*Pi]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [170 / 210] 170/210]: [[2.965939338+3.157233717*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}-10.37113929-12.75980866*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [182 / 210]
{Complex[2.9659393403344363, 3.1572337219665294] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-10.371139260352981, -12.759808690998973] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = (-1)^{mn}\modBesselK{n}@{z}+(-1)^{n(m-1)-1}m\pi i\modBesselI{n}@{z}} | BesselK(n, z*exp(m*Pi*I)) = (- 1)^(m*n)* BesselK(n, z)+(- 1)^(n*(m - 1)- 1)* m*Pi*I*BesselI(n, z) |
BesselK[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)* BesselK[n, z]+(- 1)^(n*(m - 1)- 1)* m*Pi*I*BesselI[n, z] |
Failure | Failure | Failed [57 / 63] 57/63]: [[-1.971501919+2.706233555*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}-.7368261646+.3579119854*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} |
Failed [48 / 63]
{Complex[-1.9715019183470535, 2.7062335550125516] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.736826162742255, 0.3579119863626685] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = +(-1)^{n(m-1)}m\modBesselK{n}@{ze^{+\pi i}}-(-1)^{nm}(m- 1)\modBesselK{n}@{z}} | BesselK(n, z*exp(m*Pi*I)) = +(- 1)^(n*(m - 1))* m*BesselK(n, z*exp(+ Pi*I))-(- 1)^(n*m)*(m - 1)* BesselK(n, z) |
BesselK[n, z*Exp[m*Pi*I]] == +(- 1)^(n*(m - 1))* m*BesselK[n, z*Exp[+ Pi*I]]-(- 1)^(n*m)*(m - 1)* BesselK[n, z] |
Failure | Failure | Failed [51 / 63] 51/63]: [[-1.971501920+2.706233556*I <- {z = 1/2*3^(1/2)+1/2*I, m = 2, n = 1}.7368261602-.357911988*I <- {z = 1/2*3^(1/2)+1/2*I, m = 2, n = 2} |
Failed [42 / 63]
{Complex[-1.9715019183470535, 2.7062335550125516] <- {Rule[m, 2], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.736826162742255, -0.3579119863626685] <- {Rule[m, 2], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = -(-1)^{n(m-1)}m\modBesselK{n}@{ze^{-\pi i}}+(-1)^{nm}(m+ 1)\modBesselK{n}@{z}} | BesselK(n, z*exp(m*Pi*I)) = -(- 1)^(n*(m - 1))* m*BesselK(n, z*exp(- Pi*I))+(- 1)^(n*m)*(m + 1)* BesselK(n, z) |
BesselK[n, z*Exp[m*Pi*I]] == -(- 1)^(n*(m - 1))* m*BesselK[n, z*Exp[- Pi*I]]+(- 1)^(n*m)*(m + 1)* BesselK[n, z] |
Failure | Failure | Failed [54 / 63] 54/63]: [[-1.971501919+2.706233556*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}-.7368261645+.357911985*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2} |
Failed [63 / 63]
{Complex[-1.9715019183470535, 2.7062335550125516] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.736826162742255, 0.3579119863626685] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.34#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{\conj{z}} = \conj{\modBesselI{\nu}@{z}}} | BesselI(nu, conjugate(z)) = conjugate(BesselI(nu, z)) |
BesselI[\[Nu], Conjugate[z]] == Conjugate[BesselI[\[Nu], z]] |
Failure | Failure | Skipped - Because timed out | Failed [28 / 70]
{Complex[-0.1457476573229447, -0.7449450592023206] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.100244133383339, 1.2347828003590728] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.34#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{\conj{z}} = \conj{\modBesselK{\nu}@{z}}} | BesselK(nu, conjugate(z)) = conjugate(BesselK(nu, z)) |
BesselK[\[Nu], Conjugate[z]] == Conjugate[BesselK[\[Nu], z]] |
Failure | Failure | Failed [28 / 70] 28/70]: [[-.3322466664+.1347267497*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}.8978926857-1.555608423*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [28 / 70]
{Complex[-0.332246666369582, 0.13472674975137633] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.23222824698313052, -0.12812607679285354] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.35.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\frac{1}{2}z(t+t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\modBesselI{m}@{z}} | exp((1)/(2)*z*(t + (t)^(- 1))) = sum((t)^(m)* BesselI(m, z), m = - infinity..infinity) |
Exp[Divide[1,2]*z*(t + (t)^(- 1))] == Sum[(t)^(m)* BesselI[m, z], {m, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Error | Skipped - Because timed out | Skipped - Because timed out |
| 10.35.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\cos@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\modBesselI{k}@{z}\cos@{k\theta}} | exp(z*cos(theta)) = BesselI(0, z)+ 2*sum(BesselI(k, z)*cos(k*theta), k = 1..infinity) |
Exp[z*Cos[\[Theta]]] == BesselI[0, z]+ 2*Sum[BesselI[k, z]*Cos[k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Successful | Skipped - Because timed out | Successful [Tested: 70] |
| 10.35.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\sin@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=0}^{\infty}(-1)^{k}\modBesselI{2k+1}@{z}\sin@{(2k+1)\theta}+2\sum_{k=1}^{\infty}(-1)^{k}\modBesselI{2k}@{z}\cos@{2k\theta}} | exp(z*sin(theta)) = BesselI(0, z)+ 2*sum((- 1)^(k)* BesselI(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity)+ 2*sum((- 1)^(k)* BesselI(2*k, z)*cos(2*k*theta), k = 1..infinity) |
Exp[z*Sin[\[Theta]]] == BesselI[0, z]+ 2*Sum[(- 1)^(k)* BesselI[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]+ 2*Sum[(- 1)^(k)* BesselI[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.35.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 = \modBesselI{0}@{z}-2\modBesselI{2}@{z}+2\modBesselI{4}@{z}-2\modBesselI{6}@{z}+\dotsb} | 1 = BesselI(0, z)- 2*BesselI(2, z)+ 2*BesselI(4, z)- 2*BesselI(6, z)+ .. |
1 == BesselI[0, z]- 2*BesselI[2, z]+ 2*BesselI[4, z]- 2*BesselI[6, z]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-9.440290591519046*^-8, -1.7199789187696823*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-9.924736610669727*^-8, -1.6360842739013975*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.35.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+ z} = \modBesselI{0}@{z}+ 2\modBesselI{1}@{z}+2\modBesselI{2}@{z}+ 2\modBesselI{3}@{z}+\dotsb} | exp(+ z) = BesselI(0, z)+ 2*BesselI(1, z)+ 2*BesselI(2, z)+ 2*BesselI(3, z)+ .. |
Exp[+ z] == BesselI[0, z]+ 2*BesselI[1, z]+ 2*BesselI[2, z]+ 2*BesselI[3, z]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-0.003384051289485407, 0.00475177611436145], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.002576303532707505, 0.004074841322498801], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.35.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{- z} = \modBesselI{0}@{z}- 2\modBesselI{1}@{z}+2\modBesselI{2}@{z}- 2\modBesselI{3}@{z}+\dotsb} | exp(- z) = BesselI(0, z)- 2*BesselI(1, z)+ 2*BesselI(2, z)- 2*BesselI(3, z)+ .. |
Exp[- z] == BesselI[0, z]- 2*BesselI[1, z]+ 2*BesselI[2, z]- 2*BesselI[3, z]+ \[Ellipsis] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-0.0024389937896763803, 0.0042567403420422645], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.0020316532349716754, 0.004934003265463338], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.37.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\modBesselK{\nu}@{z}| < |\modBesselK{\mu}@{z}|} | abs(BesselK(nu, z)) < abs(BesselK(mu, z)) |
Abs[BesselK[\[Nu], z]] < Abs[BesselK[\[Mu], z]] |
Failure | Failure | Failed [204 / 300] 204/300]: [[.6496143723 < .6496143723 <- {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}3.110500858 < 3.110500858 <- {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} |
Failed [184 / 300]
{False <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}False <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} |
| 10.38.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{+\nu}@{z}}{\nu} = +\modBesselI{+\nu}@{z}\ln@{\tfrac{1}{2}z}-(\tfrac{1}{2}z)^{+\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1+\nu}}{\EulerGamma@{k+1+\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!}} | diff(BesselI(+ nu, z), nu) = + BesselI(+ nu, z)*ln((1)/(2)*z)-((1)/(2)*z)^(+ nu)* sum((Psi(k + 1 + nu))/(GAMMA(k + 1 + nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselI[+ \[Nu], z], \[Nu]] == + BesselI[+ \[Nu], z]*Log[Divide[1,2]*z]-(Divide[1,2]*z)^(+ \[Nu])* Sum[Divide[PolyGamma[k + 1 + \[Nu]],Gamma[k + 1 + \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [7 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -2]} |
| 10.38.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{-\nu}@{z}}{\nu} = -\modBesselI{-\nu}@{z}\ln@{\tfrac{1}{2}z}+(\tfrac{1}{2}z)^{-\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1-\nu}}{\EulerGamma@{k+1-\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!}} | diff(BesselI(- nu, z), nu) = - BesselI(- nu, z)*ln((1)/(2)*z)+((1)/(2)*z)^(- nu)* sum((Psi(k + 1 - nu))/(GAMMA(k + 1 - nu))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity) |
D[BesselI[- \[Nu], z], \[Nu]] == - BesselI[- \[Nu], z]*Log[Divide[1,2]*z]+(Divide[1,2]*z)^(- \[Nu])* Sum[Divide[PolyGamma[k + 1 - \[Nu]],Gamma[k + 1 - \[Nu]]]*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [7 / 70]
{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 2]} |
| 10.38.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselK{\nu}@{z}}{\nu} = \tfrac{1}{2}\pi\csc@{\nu\pi}\*\left(\pderiv{\modBesselI{-\nu}@{z}}{\nu}-\pderiv{\modBesselI{\nu}@{z}}{\nu}\right)-\pi\cot@{\nu\pi}\modBesselK{\nu}@{z}} | diff(BesselK(nu, z), nu) = (1)/(2)*Pi*csc(nu*Pi)*(diff(BesselI(- nu, z), nu)- diff(BesselI(nu, z), nu))- Pi*cot(nu*Pi)*BesselK(nu, z) |
D[BesselK[\[Nu], z], \[Nu]] == Divide[1,2]*Pi*Csc[\[Nu]*Pi]*(D[BesselI[- \[Nu], z], \[Nu]]- D[BesselI[\[Nu], z], \[Nu]])- Pi*Cot[\[Nu]*Pi]*BesselK[\[Nu], z] |
Successful | Failure | - | Successful [Tested: 7] |
| 10.39#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh@@{z}} | BesselI((1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* sinh(z) |
BesselI[Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Sinh[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.39#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\cosh@@{z}} | BesselI(-(1)/(2), z) = ((2)/(Pi*z))^((1)/(2))* cosh(z) |
BesselI[-Divide[1,2], z] == (Divide[2,Pi*z])^(Divide[1,2])* Cosh[z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.39.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{1}{2}}@{z} = \modBesselK{-\frac{1}{2}}@{z}} | BesselK((1)/(2), z) = BesselK(-(1)/(2), z) |
BesselK[Divide[1,2], z] == BesselK[-Divide[1,2], z] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 7] |
| 10.39.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\frac{1}{2}}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}} | BesselK(-(1)/(2), z) = ((Pi)/(2*z))^((1)/(2))* exp(- z) |
BesselK[-Divide[1,2], z] == (Divide[Pi,2*z])^(Divide[1,2])* Exp[- z] |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.39.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{1}{4}}@{z} = \pi^{\frac{1}{2}}z^{-\frac{1}{4}}\paraU@{0}{2z^{\frac{1}{2}}}} | BesselK((1)/(4), z) = (Pi)^((1)/(2))* (z)^(-(1)/(4))* CylinderU(0, 2*(z)^((1)/(2))) |
BesselK[Divide[1,4], z] == (Pi)^(Divide[1,2])* (z)^(-Divide[1,4])* ParabolicCylinderD[- 1/2 -(0), 2*(z)^(Divide[1,2])] |
Successful | Failure | - | Successful [Tested: 7] |
| 10.39.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{3}{4}}@{z} = \tfrac{1}{2}\pi^{\frac{1}{2}}z^{-\frac{3}{4}}\left(\tfrac{1}{2}\paraU@{1}{2z^{\frac{1}{2}}}+\paraU@{-1}{2z^{\frac{1}{2}}}\right)} | BesselK((3)/(4), z) = (1)/(2)*(Pi)^((1)/(2))* (z)^(-(3)/(4))*((1)/(2)*CylinderU(1, 2*(z)^((1)/(2)))+ CylinderU(- 1, 2*(z)^((1)/(2)))) |
BesselK[Divide[3,4], z] == Divide[1,2]*(Pi)^(Divide[1,2])* (z)^(-Divide[3,4])*(Divide[1,2]*ParabolicCylinderD[- 1/2 -(1), 2*(z)^(Divide[1,2])]+ ParabolicCylinderD[- 1/2 -(- 1), 2*(z)^(Divide[1,2])]) |
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.39.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{+ z}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{- 2z}} | BesselI(nu, z) = (((1)/(2)*z)^(nu)* exp(+ z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, - 2*z) |
BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu]* Exp[+ z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, - 2*z] |
Failure | Successful | Failed [7 / 56] 7/56]: [[-.800260207-.3396157390*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}-.4588638571-.5759587792*I <- {nu = -1/2, z = -1/2+1/2*I*3^(1/2)} |
Failed [7 / 56]
{Complex[-0.8002602062152042, -0.3396157389151986] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}Complex[-0.45886385712966904, -0.5759587792371148] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]} |
| 10.39.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- z}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2z}} | BesselI(nu, z) = (((1)/(2)*z)^(nu)* exp(- z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, + 2*z) |
BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu]* Exp[- z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, + 2*z] |
Successful | Successful | Skip - symbolical successful subtest | Failed [7 / 56]
{Complex[0.8002602062152032, 0.3396157389151989] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}Complex[0.4588638571296689, 0.575958779237115] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]} |
| 10.39.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \pi^{\frac{1}{2}}(2z)^{\nu}e^{-z}\KummerconfhyperU@{\nu+\tfrac{1}{2}}{2\nu+1}{2z}} | BesselK(nu, z) = (Pi)^((1)/(2))*(2*z)^(nu)* exp(- z)*KummerU(nu +(1)/(2), 2*nu + 1, 2*z) |
BesselK[\[Nu], z] == (Pi)^(Divide[1,2])*(2*z)^\[Nu]* Exp[- z]*HypergeometricU[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, 2*z] |
Successful | Successful | - | Successful [Tested: 70] |
| 10.39.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{2z}}{2^{2\nu}\EulerGamma@{\nu+1}}} | BesselI(nu, z) = ((2*z)^(-(1)/(2))* WhittakerM(0, nu, 2*z))/((2)^(2*nu)* GAMMA(nu + 1)) |
BesselI[\[Nu], z] == Divide[(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], 2*z],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]] |
Successful | Successful | - | Successful [Tested: 7] |
| 10.39.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}\WhittakerconfhyperW{0}{\nu}@{2z}} | BesselK(nu, z) = ((Pi)/(2*z))^((1)/(2))* WhittakerW(0, nu, 2*z) |
BesselK[\[Nu], z] == (Divide[Pi,2*z])^(Divide[1,2])* WhittakerW[0, \[Nu], 2*z] |
Failure | Failure | Successful [Tested: 70] | Successful [Tested: 70] |
| 10.39.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+1}}\genhyperF{0}{1}@{-}{\nu+1}{\tfrac{1}{4}z^{2}}} | BesselI(nu, z) = (((1)/(2)*z)^(nu))/(GAMMA(nu + 1))*hypergeom([-], [nu + 1], (1)/(4)*(z)^(2)) |
BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+ 1]]*HypergeometricPFQ[{-}, {\[Nu]+ 1}, Divide[1,4]*(z)^(2)] |
Error | Failure | - | Error |
| 10.40.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right)} | BesselK(nu, z) = ((Pi)/(2*z))^((1)/(2))* exp(- z)*(sum((a[k]*(nu))/((z)^(k)), k = 0..ell - 1)+ R[ell]*(nu , z)) |
BesselK[\[Nu], z] == (Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*(Sum[Divide[Subscript[a, k]*(\[Nu]),(z)^(k)], {k, 0, \[ScriptL]- 1}, GenerateConditions->None]+ Subscript[R, \[ScriptL]]*(\[Nu], z)) |
Failure | Failure | Error | Error |
| 10.41.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = (1+z^{2})^{-\frac{1}{2}}} | p = (1 + (z)^(2))^(-(1)/(2)) |
p == (1 + (z)^(2))^(-Divide[1,2]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.41#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{1}(p) = \tfrac{1}{24}(3p-5p^{3})} | U[1]*(p) = (1)/(24)*(3*p - 5*(p)^(3)) |
Subscript[U, 1]*(p) == Divide[1,24]*(3*p - 5*(p)^(3)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.41#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{2}(p) = \tfrac{1}{1152}(81p^{2}-462p^{4}+385p^{6})} | U[2]*(p) = (1)/(1152)*(81*(p)^(2)- 462*(p)^(4)+ 385*(p)^(6)) |
Subscript[U, 2]*(p) == Divide[1,1152]*(81*(p)^(2)- 462*(p)^(4)+ 385*(p)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.41#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{3}(p) = \tfrac{1}{4\;14720}\*(30375p^{3}-3\;69603p^{5}+7\;65765p^{7}-4\;25425p^{9})} | U[3]*(p) = (1)/(414720)*(30375*(p)^(3)- 369603*(p)^(5)+ 765765*(p)^(7)- 425425*(p)^(9)) |
Subscript[U, 3]*(p) == Divide[1,414720]*(30375*(p)^(3)- 369603*(p)^(5)+ 765765*(p)^(7)- 425425*(p)^(9)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.41#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{1}(p) = \tfrac{1}{24}(-9p+7p^{3})} | V[1]*(p) = (1)/(24)*(- 9*p + 7*(p)^(3)) |
Subscript[V, 1]*(p) == Divide[1,24]*(- 9*p + 7*(p)^(3)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.41#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{2}(p) = \tfrac{1}{1152}(-135p^{2}+594p^{4}-455p^{6})} | V[2]*(p) = (1)/(1152)*(- 135*(p)^(2)+ 594*(p)^(4)- 455*(p)^(6)) |
Subscript[V, 2]*(p) == Divide[1,1152]*(- 135*(p)^(2)+ 594*(p)^(4)- 455*(p)^(6)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.41#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{3}(p) = \tfrac{1}{4\;14720}\*(-42525p^{3}+4\;51737p^{5}-8\;83575p^{7}+4\;75475p^{9})} | V[3]*(p) = (1)/(414720)*(- 42525*(p)^(3)+ 451737*(p)^(5)- 883575*(p)^(7)+ 475475*(p)^(9)) |
Subscript[V, 3]*(p) == Divide[1,414720]*(- 42525*(p)^(3)+ 451737*(p)^(5)- 883575*(p)^(7)+ 475475*(p)^(9)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.43.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\modBesselI{0}@{t}-1}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x}} | int((BesselI(0, t)- 1)/(t), t = 0..x) = (1)/(2)*sum((- 1)^(k - 1)*(Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselI(k, x), k = 1..infinity) |
Integrate[Divide[BesselI[0, t]- 1,t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*Sum[(- 1)^(k - 1)*Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselI[k, x], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Failure | Successful [Tested: 3] | Failed [3 / 3]
{Plus[DirectedInfinity[-1], Times[-0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.75, k], BesselI[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}Plus[DirectedInfinity[-1], Times[-0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.25, k], BesselI[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]} |
| 10.43.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x} = \frac{2}{x}\sum_{k=0}^{\infty}(-1)^{k}(2k+3)(\digamma@{k+2}-\digamma@{1})\modBesselI{2k+3}@{x}} | (1)/(2)*sum((- 1)^(k - 1)*(Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselI(k, x), k = 1..infinity) = (2)/(x)*sum((- 1)^(k)*(2*k + 3)*(Psi(k + 2)- Psi(1))* BesselI(2*k + 3, x), k = 0..infinity) |
Divide[1,2]*Sum[(- 1)^(k - 1)*Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselI[k, x], {k, 1, Infinity}, GenerateConditions->None] == Divide[2,x]*Sum[(- 1)^(k)*(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselI[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Successful [Tested: 3] | Failed [3 / 3]
{Plus[Times[0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.75, k], BesselI[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.3333333333333333, NSum[Times[Power[-1, k], Plus[3, Times[2, k]], BesselI[Plus[3, Times[2, k]], 1.5], Plus[EulerGamma, PolyGamma[0, Plus[2, k]]]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}Plus[Times[0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.25, k], BesselI[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-4.0, NSum[Times[Power[-1, k], Plus[3, Times[2, k]], BesselI[Plus[3, Times[2, k]], 0.5], Plus[EulerGamma, PolyGamma[0, Plus[2, k]]]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]} |
| 10.43.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\modBesselK{0}@{t}}{t}\diff{t} = \frac{1}{2}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi^{2}}{24}-\sum_{k=1}^{\infty}\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}} | int((BesselK(0, t))/(t), t = x..infinity) = (1)/(2)*(ln((1)/(2)*x)+ gamma)^(2)+((Pi)^(2))/(24)- sum((Psi(k + 1)+(1)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity) |
Integrate[Divide[BesselK[0, t],t], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[Divide[1,2]*x]+ EulerGamma)^(2)+Divide[(Pi)^(2),24]- Sum[(PolyGamma[k + 1]+Divide[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 3] | Skipped - Because timed out |
| 10.43.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{-t}\modBesselI{n}@{t}\diff{t} = xe^{-x}(\modBesselI{0}@{x}+\modBesselI{1}@{x})+n(e^{-x}\modBesselI{0}@{x}-1)+2e^{-x}\sum_{k=1}^{n-1}(n-k)\modBesselI{k}@{x}} | int(exp(- t)*BesselI(n, t), t = 0..x) = x*exp(- x)*(BesselI(0, x)+ BesselI(1, x))+ n*(exp(- x)*BesselI(0, x)- 1)+ 2*exp(- x)*sum((n - k)* BesselI(k, x), k = 1..n - 1) |
Integrate[Exp[- t]*BesselI[n, t], {t, 0, x}, GenerateConditions->None] == x*Exp[- x]*(BesselI[0, x]+ BesselI[1, x])+ n*(Exp[- x]*BesselI[0, x]- 1)+ 2*Exp[- x]*Sum[(n - k)* BesselI[k, x], {k, 1, n - 1}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 3] | Failed [2 / 3]
{Plus[1.0269197346695518, Times[-0.44626032029685964, Plus[-4.940169569318671, Times[3.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[1.5, []], Times[Plus[-2, Times[-2, ], Times[-1, 1.5]], [Plus[1, ]]], Times[Plus[2, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[1.5, [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], BesselI[0, 1.5]], Equal[[2], Plus[BesselI[0, 1.5], BesselI[1, 1.5]]]}]][3.0]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], 1.5, []], Times[-1, Plus[2, ], Plus[Times[2, ], 1.5], [Plus[1, ]]], Times[, Plus[4, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[, 1.5, [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], BesselI[1, 1.5]], Equal[[3], Plus[Times[2, Power[1.5, -1], Plus[Times[1.5, BesselI[0, 1.5]], Times[-2, BesselI[1, 1.5]]]], BesselI[1, 1.5]]]}]][3.0]]]]], {Rule[n, 3], Rule[x, 1.5]}Plus[0.6643873281588137, Times[-1.2130613194252668, Plus[-3.19045011222397, Times[3.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[0.5, []], Times[Plus[-2, Times[-2, ], Times[-1, 0.5]], [Plus[1, ]]], Times[Plus[2, Times[2, ], Times[-1, 0.5]], [Plus[2, ]]], Times[0.5, [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], BesselI[0, 0.5]], Equal[[2], Plus[BesselI[0, 0.5], BesselI[1, 0.5]]]}]][3.0]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], 0.5, []], Times[-1, Plus[2, ], Plus[Times[2, ], 0.5], [Plus[1, ]]], Times[, Plus[4, Times[2, ], Times[-1, 0.5]], [Plus[2, ]]], Times[, 0.5, [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], BesselI[1, 0.5]], Equal[[3], Plus[Times[2, Power[0.5, -1], Plus[Times[0.5, BesselI[0, 0.5]], Times[-2, BesselI[1, 0.5]]]], BesselI[1, 0.5]]]}]][3.0]]]]], {Rule[n, 3], Rule[x, 0.5]} |
| 10.43.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}-\modBesselI{\nu+1}@{x})} | int(exp(+ t)*(t)^(nu)* BesselI(nu, t), t = 0..x) = (exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselI(nu, x)- BesselI(nu + 1, x)) |
Integrate[Exp[+ t]*(t)^\[Nu]* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]+ 1, x]) |
Failure | Successful | Successful [Tested: 15] | Successful [Tested: 15] |
| 10.43.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}+\modBesselI{\nu+1}@{x})} | int(exp(- t)*(t)^(nu)* BesselI(nu, t), t = 0..x) = (exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselI(nu, x)+ BesselI(nu + 1, x)) |
Integrate[Exp[- t]*(t)^\[Nu]* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]+ 1, x]) |
Failure | Successful | Skipped - Because timed out | Successful [Tested: 15] |
| 10.43.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{+ x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}-\modBesselI{\nu-1}@{x})-\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}} | int(exp(+ t)*(t)^(- nu)* BesselI(nu, t), t = 0..x) = -(exp(+ x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)- BesselI(nu - 1, x))-((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu)) |
Integrate[Exp[+ t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[+ x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]- 1, x])-Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]] |
Failure | Successful | - | Failed [3 / 12]
{0.39894228040143315 <- {Rule[x, 1.5], Rule[ν, 1.5]}0.39894228040143254 <- {Rule[x, 0.5], Rule[ν, 1.5]} |
| 10.43.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{- x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}+\modBesselI{\nu-1}@{x})+\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}} | int(exp(- t)*(t)^(- nu)* BesselI(nu, t), t = 0..x) = -(exp(- x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)+ BesselI(nu - 1, x))+((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu)) |
Integrate[Exp[- t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[- x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]- 1, x])+Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]] |
Failure | Successful | - | Successful [Tested: 12] |
| 10.43.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}+\modBesselK{\nu+1}@{x})-\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}} | int(exp(+ t)*(t)^(nu)* BesselK(nu, t), t = 0..x) = (exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)+ BesselK(nu + 1, x))-((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1) |
Integrate[Exp[+ t]*(t)^\[Nu]* BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]+ 1, x])-Divide[(2)^\[Nu]* Gamma[\[Nu]+ 1],2*\[Nu]+ 1] |
Failure | Error | - | Failed [9 / 15]
{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 1.5]}DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 0.5]} |
| 10.43.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}-\modBesselK{\nu+1}@{x})+\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}} | int(exp(- t)*(t)^(nu)* BesselK(nu, t), t = 0..x) = (exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)- BesselK(nu + 1, x))+((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1) |
Integrate[Exp[- t]*(t)^\[Nu]* BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]- BesselK[\[Nu]+ 1, x])+Divide[(2)^\[Nu]* Gamma[\[Nu]+ 1],2*\[Nu]+ 1] |
Failure | Successful | - | Failed [3 / 15]
{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 2]}DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]} |
| 10.43.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}e^{t}t^{-\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{x}x^{-\nu+1}}{2\nu-1}(\modBesselK{\nu}@{x}+\modBesselK{\nu-1}@{x})} | int(exp(t)*(t)^(- nu)* BesselK(nu, t), t = x..infinity) = (exp(x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselK(nu, x)+ BesselK(nu - 1, x)) |
Integrate[Exp[t]*(t)^(- \[Nu])* BesselK[\[Nu], t], {t, x, Infinity}, GenerateConditions->None] == Divide[Exp[x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]- 1, x]) |
Failure | Successful | - | Failed [3 / 9]
{Indeterminate <- {Rule[x, 1.5], Rule[ν, 2]}DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]} |
| 10.43.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselK{\nu}@{t}\diff{t} = \tfrac{1}{2}\pi\sec@{\tfrac{1}{2}\pi\nu}} | int(BesselK(nu, t), t = 0..infinity) = (1)/(2)*Pi*sec((1)/(2)*Pi*nu) |
Integrate[BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*Sec[Divide[1,2]*Pi*\[Nu]] |
Successful | Successful | - | Successful [Tested: 6] |
| 10.43.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}\modBesselK{\nu}@{t}\diff{t} = 2^{\mu-2}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu}} | int((t)^(mu - 1)* BesselK(nu, t), t = 0..infinity) = (2)^(mu - 2)* GAMMA((1)/(2)*mu -(1)/(2)*nu)*GAMMA((1)/(2)*mu +(1)/(2)*nu) |
Integrate[(t)^(\[Mu]- 1)* BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == (2)^(\[Mu]- 2)* Gamma[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]] |
Successful | Successful | - | Successful [Tested: 18] |
| 10.43.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{at}\modBesselK{0}@{t}\diff{t} = \frac{\pi}{2(1+a^{2})^{\frac{1}{2}}}} | int(cos(a*t)*BesselK(0, t), t = 0..infinity) = (Pi)/(2*(1 + (a)^(2))^((1)/(2))) |
Integrate[Cos[a*t]*BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2*(1 + (a)^(2))^(Divide[1,2])] |
Successful | Error | - | Successful [Tested: 6] |
| 10.43.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\sin@{at}\modBesselK{0}@{t}\diff{t} = \frac{\asinh@@{a}}{(1+a^{2})^{\frac{1}{2}}}} | int(sin(a*t)*BesselK(0, t), t = 0..infinity) = (arcsinh(a))/((1 + (a)^(2))^((1)/(2))) |
Integrate[Sin[a*t]*BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[ArcSinh[a],(1 + (a)^(2))^(Divide[1,2])] |
Failure | Successful | Successful [Tested: 0] | Successful [Tested: 6] |
| 10.43.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselI{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}} | int(BesselI(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(2*p)*exp(((b)^(2))/(8*(p)^(2)))*BesselI((1)/(2)*nu, ((b)^(2))/(8*(p)^(2))) |
Integrate[BesselI[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],2*p]*Exp[Divide[(b)^(2),8*(p)^(2)]]*BesselI[Divide[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]] |
Failure | Error | Failed [228 / 300] 228/300]: [[-.7585567167+3.675115279*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I}-.9489546609+2.381017603*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = -1/2*3^(1/2)-1/2*I} |
Failed [152 / 300]
{Complex[-0.19039794459564638, -1.294097675814569] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[2.992047945390181, -4.249025046528451] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.43.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselK{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{4p}\sec@{\tfrac{1}{2}\pi\nu}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselK{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}} | int(BesselK(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(4*p)*sec((1)/(2)*Pi*nu)*exp(((b)^(2))/(8*(p)^(2)))*BesselK((1)/(2)*nu, ((b)^(2))/(8*(p)^(2))) |
Integrate[BesselK[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],4*p]*Sec[Divide[1,2]*Pi*\[Nu]]*Exp[Divide[(b)^(2),8*(p)^(2)]]*BesselK[Divide[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]] |
Failure | Error | Failed [144 / 288] 144/288]: [[-.4056916296-1.844454275*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I}-.2830456904e-1-1.996429597*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 3/2} |
Failed [144 / 288]
{Complex[0.40569163152223653, 1.8444542715605226] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.4232355421098407, -0.8203643961026106] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.43.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\modBesselI{0}@{at}\modBesselK{0}@{at}\diff{t} = \frac{1}{4p^{2}}\exp@{\frac{a^{2}}{2p^{2}}}\modBesselK{0}@{\frac{a^{2}}{2p^{2}}}} | int(t*exp(- (p)^(2)* (t)^(2))*BesselI(0, a*t)*BesselK(0, a*t), t = 0..infinity) = (1)/(4*(p)^(2))*exp(((a)^(2))/(2*(p)^(2)))*BesselK(0, ((a)^(2))/(2*(p)^(2))) |
Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselI[0, a*t]*BesselK[0, a*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,4*(p)^(2)]*Exp[Divide[(a)^(2),2*(p)^(2)]]*BesselK[0, Divide[(a)^(2),2*(p)^(2)]] |
Failure | Error | Skipped - Because timed out | Successful [Tested: 48] |
| 10.44#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \sum_{k=0}^{\infty}\frac{z^{k}}{k!}\BesselJ{\nu+k}@{z}} | BesselI(nu, z) = sum(((z)^(k))/(factorial(k))*BesselJ(nu + k, z), k = 0..infinity) |
BesselI[\[Nu], z] == Sum[Divide[(z)^(k),(k)!]*BesselJ[\[Nu]+ k, z], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Successful | Skipped - Because timed out | Successful [Tested: 70] |
| 10.44#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \sum_{k=0}^{\infty}(-1)^{k}\frac{z^{k}}{k!}\modBesselI{\nu+k}@{z}} | BesselJ(nu, z) = sum((- 1)^(k)*((z)^(k))/(factorial(k))*BesselI(nu + k, z), k = 0..infinity) |
BesselJ[\[Nu], z] == Sum[(- 1)^(k)*Divide[(z)^(k),(k)!]*BesselI[\[Nu]+ k, z], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [70 / 70]
{Plus[Complex[0.4358908643715884, -0.07192294931339177], Times[-1.0, NSum[Times[Power[-1, k], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[1.0679098760861825, 0.09257666026367889], Times[-1.0, NSum[Times[Power[-1, k], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], BesselI[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.44.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\tfrac{1}{2}z\right)^{\nu} = \sum_{k=0}^{\infty}(-1)^{k}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\modBesselI{\nu+2k}@{z}} | ((1)/(2)*z)^(nu) = sum((- 1)^(k)*((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselI(nu + 2*k, z), k = 0..infinity) |
(Divide[1,2]*z)^\[Nu] == Sum[(- 1)^(k)*Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselI[\[Nu]+ 2*k, z], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | - | Failed [7 / 7]
{Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1]}Plus[Complex[-0.2499999999999999, 0.43301270189221935], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 1]} |
| 10.44.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\frac{\modBesselI{2k}@{z}}{k}} | BesselK(0, z) = -(ln((1)/(2)*z)+ gamma)* BesselI(0, z)+ 2*sum((BesselI(2*k, z))/(k), k = 1..infinity) |
BesselK[0, z] == -(Log[Divide[1,2]*z]+ EulerGamma)* BesselI[0, z]+ 2*Sum[Divide[BesselI[2*k, z],k], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Successful | Successful [Tested: 7] | Successful [Tested: 7] |
| 10.44.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{z} = \frac{n!(\tfrac{1}{2}z)^{-n}}{2}\sum_{k=0}^{n-1}(-1)^{k}\frac{(\tfrac{1}{2}z)^{k}\modBesselI{k}@{z}}{k!(n-k)}+(-1)^{n-1}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\modBesselI{n}@{z}+(-1)^{n}\sum_{k=1}^{\infty}\frac{(n+2k)\modBesselI{n+2k}@{z}}{k(n+k)}} | BesselK(n, z) = (factorial(n)*((1)/(2)*z)^(- n))/(2)*sum((- 1)^(k)*(((1)/(2)*z)^(k)* BesselI(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(- 1)^(n - 1)*(ln((1)/(2)*z)- Psi(n + 1))* BesselI(n, z)+(- 1)^(n)* sum(((n + 2*k)* BesselI(n + 2*k, z))/(k*(n + k)), k = 1..infinity) |
BesselK[n, z] == Divide[(n)!*(Divide[1,2]*z)^(- n),2]*Sum[(- 1)^(k)*Divide[(Divide[1,2]*z)^(k)* BesselI[k, z],(k)!*(n - k)], {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n - 1)*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselI[n, z]+(- 1)^(n)* Sum[Divide[(n + 2*k)* BesselI[n + 2*k, z],k*(n + k)], {k, 1, Infinity}, GenerateConditions->None] |
Failure | Error | - | Failed [21 / 21]
{Plus[Complex[1.084080291505059, -0.3914662527648858], NSum[Times[Power[k, -1], Power[Plus[1, k], -1], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]], Times[Complex[-0.8660254037844387, 0.49999999999999994], DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, Plus[Times[-1, ], 1], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], []], Times[Plus[4, Times[12, ], Times[12, Power[, 2]], Times[4, Power[, 3]], Times[-4, 1], Times[-8, , 1], Times[-4, Power[, 2], 1], Times[-1, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[1, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], [Plus[1, ]]], Times[4, Plus[1, ], Plus[-5, Times[-6, ], Times[-2, Power[, 2]], Times[3, 1], Times[2, , 1]], [Plus[2, ]]], Times[-4, Plus[1, ], Plus[2, ], Plus[-2, Times[-1, ], 1], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Power[1, -1], BesselI[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Power[1, -1], BesselI[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[-1, 2], Power[Plus[-1, 1], -1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], BesselI[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.001928095904955185, 0.0030033056761246957], Times[-1.0, NSum[Times[Power[k, -1], Power[Plus[2, k], -1], Plus[2, Times[2, k]], BesselI[Plus[2, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.45.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(\nu^{2}-x^{2})w = 0} | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((nu)^(2)- (x)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+(\[Nu]^(2)- (x)^(2))* w == 0 |
Failure | Failure | Failed [240 / 300] 240/300]: [[-1.948557159-.1249999996*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}-.2165063507+.8750000006*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [240 / 300]
{Complex[-1.948557158514987, -0.12499999999999989] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.9485571585149875, -2.125] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{\nu}@{x} = \realpart@{\modBesselI{i\nu}@{x}}} | Re(BesselI(I*(nu), x)) = Re(BesselI(I*nu, x)) |
Re[BesselI[I*\[Nu], x]] == Re[BesselI[I*\[Nu], x]] |
Successful | Successful | - | Successful [Tested: 30] |
| 10.45.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{\nu}@{x} = \modBesselK{i\nu}@{x}} | BesselK(I*(nu), x) = BesselK(I*nu, x) |
BesselK[I*\[Nu], x] == BesselK[I*\[Nu], x] |
Successful | Successful | - | Successful [Tested: 30] |
| 10.45.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{-\nu}@{x} = \modBesselIimag{\nu}@{x}} | Re(BesselI(I*(- nu), x)) = Re(BesselI(I*(nu), x)) |
Re[BesselI[I*- \[Nu], x]] == Re[BesselI[I*\[Nu], x]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.45.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{-\nu}@{x} = \modBesselKimag{\nu}@{x}} | BesselK(I*(- nu), x) = BesselK(I*(nu), x) |
BesselK[I*- \[Nu], x] == BesselK[I*\[Nu], x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.45.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselKimag{\nu}@{x},\modBesselIimag{\nu}@{x}} = 1/x} | (BesselK(I*(nu), x))*diff(Re(BesselI(I*(nu), x)), x)-diff(BesselK(I*(nu), x), x)*(Re(BesselI(I*(nu), x))) = 1/ x |
Wronskian[{BesselK[I*\[Nu], x], Re[BesselI[I*\[Nu], x]]}, x] == 1/ x |
Failure | Failure | Error | Failed [30 / 30]
{Plus[-0.6666666666666666, Times[0.5, Plus[Complex[1.0700115379721733, -0.3754447148158467], Times[Complex[0.1636629185333998, 0.09141848176750039], Derivative[1][Re][Complex[2.445786867824693, 0.6492150843755028]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[-0.6666666666666666, Times[0.5, Plus[Complex[0.8415452902387464, 0.2726729041814867], Times[Complex[0.3412924192180222, 0.19179892830603273], Derivative[1][Re][Complex[1.3137906770541619, -0.7251169608509622]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.45.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselKimag{0}@{x} = \modBesselK{0}@{x}} | BesselK(I*(0), x) = BesselK(0, x) |
BesselK[I*0, x] == BesselK[0, x] |
Successful | Successful | - | Successful [Tested: 3] |
| 10.47.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}+\left(z^{2}-n(n+1)\right)w = 0} | (z)^(2)* diff(w, [z$(2)])+ 2*z*diff(w, z)+((z)^(2)- n*(n + 1))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]+((z)^(2)- n*(n + 1))* w == 0 |
Failure | Failure | Failed [210 / 210] 210/210]: [[-1.732050808+.3733632160e-9*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}-5.196152424-2.000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} |
Failed [210 / 210]
{Complex[-1.7320508075688772, 1.1102230246251565*^-16] <- {Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-5.196152422706633, -1.9999999999999996] <- {Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}-\left(z^{2}+n(n+1)\right)w = 0} | (z)^(2)* diff(w, [z$(2)])+ 2*z*diff(w, z)-((z)^(2)+ n*(n + 1))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]-((z)^(2)+ n*(n + 1))* w == 0 |
Failure | Failure | Failed [210 / 210] 210/210]: [[-1.732050808-2.000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}-5.196152424-4.000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} |
Failed [210 / 210]
{Complex[-1.7320508075688776, -1.9999999999999998] <- {Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-5.196152422706632, -3.9999999999999996] <- {Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z}} | Error |
SphericalBesselJ[n, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z] |
Error | Failure | Skip - symbolical successful subtest | Successful [Tested: 21] |
| 10.47.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z} = (-1)^{n}\sqrt{\tfrac{1}{2}\pi/z}\BesselY{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*BesselJ(n +(1)/(2), z) = (- 1)^(n)*sqrt((1)/(2)*Pi/ z)*BesselY(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z] == (- 1)^(n)*Sqrt[Divide[1,2]*Pi/ z]*BesselY[- n -Divide[1,2], z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.47.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z}} | Error |
SphericalBesselY[n, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z] |
Error | Failure | Skip - symbolical successful subtest | Successful [Tested: 21] |
| 10.47.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z} = (-1)^{n+1}\sqrt{\tfrac{1}{2}\pi/z}\BesselJ{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*BesselY(n +(1)/(2), z) = (- 1)^(n + 1)*sqrt((1)/(2)*Pi/ z)*BesselJ(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z] == (- 1)^(n + 1)*Sqrt[Divide[1,2]*Pi/ z]*BesselJ[- n -Divide[1,2], z] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 10.47.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z}} | Error |
SphericalHankelH1[n, z] == Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z] |
Error | Failure | - | Successful [Tested: 21] |
| 10.47.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z} = (-1)^{n+1}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*HankelH1(n +(1)/(2), z) = (- 1)^(n + 1)* I*sqrt((1)/(2)*Pi/ z)*HankelH1(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z] == (- 1)^(n + 1)* I*Sqrt[Divide[1,2]*Pi/ z]*HankelH1[- n -Divide[1,2], z] |
Successful | Failure | - | Successful [Tested: 21] |
| 10.47.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z}} | Error |
SphericalHankelH2[n, z] == Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z] |
Error | Failure | - | Successful [Tested: 21] |
| 10.47.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z} = (-1)^{n}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*HankelH2(n +(1)/(2), z) = (- 1)^(n)* I*sqrt((1)/(2)*Pi/ z)*HankelH2(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z] == (- 1)^(n)* I*Sqrt[Divide[1,2]*Pi/ z]*HankelH2[- n -Divide[1,2], z] |
Successful | Failure | - | Successful [Tested: 21] |
| 10.47.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{n+\frac{1}{2}}@{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == Sqrt[Divide[1,2]*Pi/ z]*BesselI[n +Divide[1,2], z] |
Error | Failure | - | Failed [20 / 21]
{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{-n-\frac{1}{2}}@{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Sqrt[Divide[1,2]*Pi/ z]*BesselI[- n -Divide[1,2], z] |
Error | Failure | - | Failed [20 / 21]
{Complex[-0.41419719140728084, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1065867555175597, 2.4569570135519543] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z] |
Error | Successful | - | Successful [Tested: 21] |
| 10.47.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{-n-\frac{1}{2}}@{z}} | sqrt((1)/(2)*Pi/ z)*BesselK(n +(1)/(2), z) = sqrt((1)/(2)*Pi/ z)*BesselK(- n -(1)/(2), z) |
Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z] == Sqrt[Divide[1,2]*Pi/ z]*BesselK[- n -Divide[1,2], z] |
Successful | Successful | - | Successful [Tested: 21] |
| 10.47#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \sphBesselJ{n}@{z}+i\sphBesselY{n}@{z}} | Error |
SphericalHankelH1[n, z] == SphericalBesselJ[n, z]+ I*SphericalBesselY[n, z] |
Error | Successful | - | Successful [Tested: 21] |
| 10.47#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \sphBesselJ{n}@{z}-i\sphBesselY{n}@{z}} | Error |
SphericalHankelH2[n, z] == SphericalBesselJ[n, z]- I*SphericalBesselY[n, z] |
Error | Successful | - | Successful [Tested: 21] |
| 10.47.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = (-1)^{n+1}\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}-\modsphBesseli{2}{n}@{z}\right)} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n + 1)*Divide[1,2]*Pi*(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]- Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]) |
Error | Failure | - | Failed [20 / 21]
{Complex[-0.7569924845794465, -0.925635877692591] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.0316385731075524, -4.1588442590402455] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = i^{-n}\sphBesselJ{n}@{iz}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (I)^(- n)* SphericalBesselJ[n, I*z] |
Error | Failure | - | Failed [20 / 21]
{Complex[0.06771919180965624, -0.2957981693651618] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.44982524194021284, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = i^{-n-1}\sphBesselY{n}@{iz}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == (I)^(- n - 1)* SphericalBesselY[n, I*z] |
Error | Failure | - | Failed [20 / 21]
{Complex[-0.41419719140728045, -0.8850762711170859] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1065867555175588, 2.456957013551956] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == -Divide[1,2]*Pi*(I)^(n)* SphericalHankelH1[n, I*z] |
Error | Failure | - | Successful [Tested: 21] |
| 10.47.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz} = -\tfrac{1}{2}\pi i^{-n}\sphHankelh{2}{n}@{-iz}} | Error |
-Divide[1,2]*Pi*(I)^(n)* SphericalHankelH1[n, I*z] == -Divide[1,2]*Pi*(I)^(- n)* SphericalHankelH2[n, - I*z] |
Error | Failure | - | Successful [Tested: 21] |
| 10.47.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphBesselJ{n}@{-z} = (-1)^{n}\sphBesselJ{n}@{z}} | Error |
SphericalBesselJ[n, - z] == (- 1)^(n)* SphericalBesselJ[n, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.47.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphBesselY{n}@{-z} = (-1)^{n+1}\sphBesselY{n}@{z}} | Error |
SphericalBesselY[n, - z] == (- 1)^(n + 1)* SphericalBesselY[n, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.47.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphHankelh{1}{n}@{-z} = (-1)^{n}\sphHankelh{2}{n}@{z}} | Error |
SphericalHankelH1[n, - z] == (- 1)^(n)* SphericalHankelH2[n, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.47.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphHankelh{2}{n}@{-z} = (-1)^{n}\sphHankelh{1}{n}@{z}} | Error |
SphericalHankelH2[n, - z] == (- 1)^(n)* SphericalHankelH1[n, z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.47.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modsphBesseli{1}{n}@{-z} = (-1)^{n}\modsphBesseli{1}{n}@{z}} | Error |
Sqrt[Divide[Pi, - z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (- 1)^(n)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.47.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modsphBesseli{2}{n}@{-z} = (-1)^{n+1}\modsphBesseli{2}{n}@{z}} | Error |
Sqrt[Divide[Pi, - z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == (- 1)^(n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.47.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{-z} = -\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}+\modsphBesseli{2}{n}@{z}\right)} | Error |
Sqrt[1/2 Pi /- z] BesselK[n + 1/2, - z] == -Divide[1,2]*Pi*(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]+ Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]) |
Error | Failure | - | Failed [21 / 21]
{Complex[-0.5442463690831921, -1.8549132335154932] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[2.444806248586177, 3.5599138449204935] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}} | Error |
SphericalBesselJ[n, z] == Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.49#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}@{z} = \frac{\sin@@{z}}{z}} | Error |
SphericalBesselJ[0, z] == Divide[Sin[z],z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.49#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{1}@{z} = \frac{\sin@@{z}}{z^{2}}-\frac{\cos@@{z}}{z}} | Error |
SphericalBesselJ[1, z] == Divide[Sin[z],(z)^(2)]-Divide[Cos[z],z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.49#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{2}@{z} = \left(-\frac{1}{z}+\frac{3}{z^{3}}\right)\sin@@{z}-\frac{3}{z^{2}}\cos@@{z}} | Error |
SphericalBesselJ[2, z] == (-Divide[1,z]+Divide[3,(z)^(3)])* Sin[z]-Divide[3,(z)^(2)]*Cos[z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.49.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}} | Error |
SphericalBesselY[n, z] == - Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.49#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{0}@{z} = -\frac{\cos@@{z}}{z}} | Error |
SphericalBesselY[0, z] == -Divide[Cos[z],z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.49#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{1}@{z} = -\frac{\cos@@{z}}{z^{2}}-\frac{\sin@@{z}}{z}} | Error |
SphericalBesselY[1, z] == -Divide[Cos[z],(z)^(2)]-Divide[Sin[z],z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.49#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{2}@{z} = \left(\frac{1}{z}-\frac{3}{z^{3}}\right)\cos@@{z}-\frac{3}{z^{2}}\sin@@{z}} | Error |
SphericalBesselY[2, z] == (Divide[1,z]-Divide[3,(z)^(3)])* Cos[z]-Divide[3,(z)^(2)]*Sin[z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.49.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = e^{iz}\sum_{k=0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
SphericalHankelH1[n, z] == Exp[I*z]*Sum[(I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Failed [210 / 210]
{Complex[-0.3966692432410339, 0.7497610210111748] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.3157223500929769, 0.5313692545383957] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = e^{-iz}\sum_{k=0}^{n}(-i)^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
SphericalHankelH2[n, z] == Exp[- I*z]*Sum[(- I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.49.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n+1}\*\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n + 1)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.49#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{0}@{z} = \frac{\sinh@@{z}}{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(0 + 1/2), 0] == Divide[Sinh[z],z] |
Error | Failure | - | Failed [7 / 7]
{Complex[-1.0789668887893185, -0.15155203743332835] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.9126970224666039, 0.13712305377128448] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.49#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{1}@{z} = -\frac{\sinh@@{z}}{z^{2}}+\frac{\cosh@@{z}}{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(1 + 1/2), 1] == -Divide[Sinh[z],(z)^(2)]+Divide[Cosh[z],z] |
Error | Failure | - | Failed [7 / 7]
{Complex[0.06771919180965646, -0.2957981693651617] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3178790653897484, -0.6062561841669247] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.49#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\sinh@@{z}-\frac{3}{z^{2}}\cosh@@{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)])* Sinh[z]-Divide[3,(z)^(2)]*Cosh[z] |
Error | Failure | - | Failed [6 / 7]
{Complex[0.44982524194021334, -0.19064547195046933] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.2843828483915114, -0.37732112452647515] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.49.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n}\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.49#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{0}@{z} = \frac{\cosh@@{z}}{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(0 + 1/2), 0] == Divide[Cosh[z],z] |
Error | Failure | - | Failed [7 / 7]
{DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.49#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{1}@{z} = -\frac{\cosh@@{z}}{z^{2}}+\frac{\sinh@@{z}}{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(1 + 1/2), 1] == -Divide[Cosh[z],(z)^(2)]+Divide[Sinh[z],z] |
Error | Failure | - | Failed [7 / 7]
{Complex[-0.41419719140728073, -0.8850762711170859] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.1181398580617885, 1.2868595835312289] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.49#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\cosh@@{z}-\frac{3}{z^{2}}\sinh@@{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)])* Cosh[z]-Divide[3,(z)^(2)]*Sinh[z] |
Error | Failure | - | Failed [6 / 7]
{Complex[1.106586755517561, 2.456957013551956] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.803584197807803, -1.2408087832280956] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.49.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \tfrac{1}{2}\pi e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Failed [210 / 210]
{Complex[-1.0260307573251746, 0.0967341401667452] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.907697530268464, -0.43148595883398677] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{0}@{z} = \tfrac{1}{2}\pi\frac{e^{-z}}{z}} | Error |
Sqrt[1/2 Pi /z] BesselK[0 + 1/2, z] == Divide[1,2]*Pi*Divide[Exp[- z],z] |
Error | Failure | - | Successful [Tested: 7] |
| 10.49#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{1}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{1}{z^{2}}\right)} | Error |
Sqrt[1/2 Pi /z] BesselK[1 + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[1,(z)^(2)]) |
Error | Failure | - | Successful [Tested: 7] |
| 10.49#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{2}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{3}{z^{2}}+\frac{3}{z^{3}}\right)} | Error |
Sqrt[1/2 Pi /z] BesselK[2 + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[3,(z)^(2)]+Divide[3,(z)^(3)]) |
Error | Failure | - | Successful [Tested: 7] |
| 10.49#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sin@@{z}}{z}} | Error |
(-Divide[1,z]*D[(z)^(n)*-Divide[1,z], z])^(n)*Divide[Sin[z],z] |
Error | Failure | - | Failed [21 / 21]
{Complex[0.28766324258243325, 0.13393934480402792] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.302013441049254, 0.9125931496973667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cos@@{z}}{z}} | Error |
SphericalBesselY[n, z] (-Divide[1,z]*D[(z)^(n)*-Divide[1,z], z])^(n)*Divide[Cos[z],z] |
Error | Failure | - | Failed [21 / 21]
{Complex[-0.9342001374760677, 0.968266641946737] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.14357960272401077, 3.9384338499123404] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sinh@@{z}}{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] (Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Sinh[z],z] |
Error | Failure | - | Failed [21 / 21]
{Complex[0.35534425318828616, -0.09521420567684166] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.19008700336701606, 0.7298484499303669] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cosh@@{z}}{z}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] (Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Cosh[z],z] |
Error | Failure | - | Failed [21 / 21]
{Complex[-0.3553442531882861, 0.09521420567684165] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.31198506093225176, 1.0184810034762684] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = (-1)^{n}\tfrac{1}{2}\pi z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{e^{-z}}{z}} | Error |
Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n)*Divide[1,2]*(Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Exp[- z],z] |
Error | Failure | - | Failed [21 / 21]
{Complex[0.3593544107322247, -1.2247601267643444] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.45891810409859557, -4.100723067341411] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}^{2}@{z}+\sphBesselY{n}^{2}@{z} = \sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}} | Error |
(SphericalBesselJ[n, z])^(2)+ (SphericalBesselY[n, z])^(2) == Sum[Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Failed [210 / 210]
{Complex[-1.2990381056766571, 0.5179491924311224] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-9.999999999999996, 1.5358983848622398] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.49#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}^{2}@{z}+\sphBesselY{0}^{2}@{z} = z^{-2}} | Error |
(SphericalBesselJ[0, z])^(2)+ (SphericalBesselY[0, z])^(2) == (z)^(- 2) |
Error | Successful | - | Successful [Tested: 7] |
| 10.49#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{1}^{2}@{z}+\sphBesselY{1}^{2}@{z} = z^{-2}+z^{-4}} | Error |
(SphericalBesselJ[1, z])^(2)+ (SphericalBesselY[1, z])^(2) == (z)^(- 2)+ (z)^(- 4) |
Error | Successful | - | Successful [Tested: 7] |
| 10.49#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{2}^{2}@{z}+\sphBesselY{2}^{2}@{z} = z^{-2}+3z^{-4}+9z^{-6}} | Error |
(SphericalBesselJ[2, z])^(2)+ (SphericalBesselY[2, z])^(2) == (z)^(- 2)+ 3*(z)^(- 4)+ 9*(z)^(- 6) |
Error | Successful | - | Successful [Tested: 7] |
| 10.49.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\modsphBesseli{1}{n}@{z}\right)^{2}-\left(\modsphBesseli{2}{n}@{z}\right)^{2} = (-1)^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}} | Error |
(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n])^(2)-(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])^(2) == (- 1)^(n + 1)* Sum[(- 1)^(k)*Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None] |
Error | Failure | - | Failed [210 / 210]
{Complex[-1.299038105676658, -0.7500000000000001] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.35182282028742856, 0.20312500000000058] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.50#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\sphBesselJ{n}@{z},\sphBesselY{n}@{z}} = z^{-2}} | Error |
Wronskian[{SphericalBesselJ[n, z], SphericalBesselY[n, z]}, z] == (z)^(- 2) |
Error | Successful | - | Successful [Tested: 21] |
| 10.50#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\sphHankelh{1}{n}@{z},\sphHankelh{2}{n}@{z}} = -2iz^{-2}} | Error |
Wronskian[{SphericalHankelH1[n, z], SphericalHankelH2[n, z]}, z] == - 2*I*(z)^(- 2) |
Error | Successful | - | Successful [Tested: 21] |
| 10.50#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesseli{2}{n}@{z}} = (-1)^{n+1}z^{-2}} | Error |
Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]}, z] == (- 1)^(n + 1)* (z)^(- 2) |
Error | Failure | - | Failed [21 / 21]
{Complex[-0.5000000000000001, 0.8660254037844386] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5000000000000001, -0.8660254037844386] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.50#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesselK{n}@{z}} = \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\} | Error |
Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] |
Error | Failure | - | Failed [21 / 21]
{Complex[0.5384915109869794, 1.7026856201657974] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.6544302063904848, -2.4451654315616667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.50#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\ = -\tfrac{1}{2}\pi z^{-2}} | Error |
Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == -Divide[1,2]*Pi*(z)^(- 2) |
Error | Failure | - | Failed [21 / 21]
{Complex[0.5161524079039588, -2.211692333258562] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[7.686727830477982, 4.996906619076774] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.50#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n+1}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+1}@{z} = z^{-2}} | Error |
SphericalBesselJ[n + 1, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 1, z] == (z)^(- 2) |
Error | Successful | - | Successful [Tested: 21] |
| 10.50#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n+2}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+2}@{z} = (2n+3)z^{-3}} | Error |
SphericalBesselJ[n + 2, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 2, z] == (2*n + 3)* (z)^(- 3) |
Error | Failure | - | Successful [Tested: 21] |
| 10.50.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}@{z}\sphBesselJ{n}@{z}+\sphBesselY{0}@{z}\sphBesselY{n}@{z} = \cos@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+2}}+\sin@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+3}}} | Error |
SphericalBesselJ[0, z]*SphericalBesselJ[n, z]+ SphericalBesselY[0, z]*SphericalBesselY[n, z] == Cos[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 3)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.51#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{n-1}(z)+f_{n+1}(z) = ((2n+1)/z)f_{n}(z)} | f[n - 1]*(z)+ f[n + 1]*(z) = ((2*n + 1)/ z)* f[n]*(z) |
Subscript[f, n - 1]*(z)+ Subscript[f, n + 1]*(z) == ((2*n + 1)/ z)* Subscript[f, n]*(z) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.51#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{n+1}f_{n}(z)) = z^{n-m+1}f_{n-m}(z)} | (diff((1)/(z), z))^(m)*((z)^(n + 1)* f[n]*(z)) = (z)^(n - m + 1)* f[n - m]*(z) |
(D[Divide[1,z], z])^(m)*((z)^(n + 1)* Subscript[f, n]*(z)) == (z)^(n - m + 1)* Subscript[f, n - m]*(z) |
Failure | Failure | Error | Failed [288 / 300]
{Complex[-0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.51#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{-n}f_{n}(z)) = (-1)^{m}z^{-n-m}f_{n+m}(z)} | (diff((1)/(z), z))^(m)*((z)^(- n)* f[n]*(z)) = (- 1)^(m)* (z)^(- n - m)* f[n + m]*(z) |
(D[Divide[1,z], z])^(m)*((z)^(- n)* Subscript[f, n]*(z)) == (- 1)^(m)* (z)^(- n - m)* Subscript[f, n + m]*(z) |
Failure | Failure | Failed [288 / 300] 288/300]: [[1.366025403-.3660254033*I <- {z = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, f[n+m] = 1/2*3^(1/2)+1/2*I, n = 1, m = 3}.9999999993-.9999999984*I <- {z = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, f[n+m] = 1/2*3^(1/2)+1/2*I, n = 2, m = 3} |
Failed [288 / 300]
{Complex[0.1339745962155613, 0.49999999999999994] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3660254037844386, 0.36602540378443865] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.51#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{n-1}(z)-g_{n+1}(z) = ((2n+1)/z)g_{n}(z)} | g[n - 1]*(z)- g[n + 1]*(z) = ((2*n + 1)/ z)* g[n]*(z) |
Subscript[g, n - 1]*(z)- Subscript[g, n + 1]*(z) == ((2*n + 1)/ z)* Subscript[g, n]*(z) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.51#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{n+1}g_{n}(z)) = z^{n-m+1}g_{n-m}(z)} | (diff((1)/(z), z))^(m)*((z)^(n + 1)* g[n]*(z)) = (z)^(n - m + 1)* g[n - m]*(z) |
(D[Divide[1,z], z])^(m)*((z)^(n + 1)* Subscript[g, n]*(z)) == (z)^(n - m + 1)* Subscript[g, n - m]*(z) |
Failure | Failure | Error | Failed [288 / 300]
{Complex[-0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.51#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{-n}g_{n}(z)) = z^{-n-m}g_{n+m}(z)} | (diff((1)/(z), z))^(m)*((z)^(- n)* g[n]*(z)) = (z)^(- n - m)* g[n + m]*(z) |
(D[Divide[1,z], z])^(m)*((z)^(- n)* Subscript[g, n]*(z)) == (z)^(- n - m)* Subscript[g, n + m]*(z) |
Failure | Failure | Failed [288 / 300] 288/300]: [[.3660254028+1.366025403*I <- {z = 1/2*3^(1/2)+1/2*I, g[n] = 1/2*3^(1/2)+1/2*I, g[n+m] = 1/2*3^(1/2)+1/2*I, n = 1, m = 3}.9999999987+.9999999996*I <- {z = 1/2*3^(1/2)+1/2*I, g[n] = 1/2*3^(1/2)+1/2*I, g[n+m] = 1/2*3^(1/2)+1/2*I, n = 2, m = 3} |
Failed [288 / 300]
{Complex[-1.8660254037844388, 0.49999999999999994] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.3660254037844388, 1.3660254037844386] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.53.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}} | Error |
SphericalBesselJ[n, z] == (z)^(n)* Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Successful [Tested: 21] |
| 10.53.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -\frac{1}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(\frac{1}{2}z^{2})^{k}}{k!}+\frac{(-1)^{n+1}}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}} | Error |
SphericalBesselY[n, z] == -Divide[1,(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[(- 1)^(n + 1),(z)^(n + 1)]*Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Successful [Tested: 21] |
| 10.53.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (z)^(n)* Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [20 / 21]
{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.53.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \frac{(-1)^{n}}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(-\frac{1}{2}z^{2})^{k}}{k!}+\frac{1}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}} | Error |
Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Divide[(- 1)^(n),(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(-Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[1,(z)^(n + 1)]*Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [20 / 21]
{Complex[-0.4141971914072808, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1065867555175597, 2.456957013551954] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.54.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{z^{n}}{2^{n+1}n!}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2n+1}\diff{\theta}} | Error |
SphericalBesselJ[n, z] == Divide[(z)^(n),(2)^(n + 1)* (n)!]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*n + 1), {\[Theta], 0, Pi}, GenerateConditions->None] |
Error | Successful | - | Successful [Tested: 21] |
| 10.54.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{(-i)^{n+1}}{2\pi}\int_{i\infty}^{(-1+,1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}} | Error |
SphericalBesselJ[n, z] == Divide[(- I)^(n + 1),2*Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 + , 1 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.54#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}} | Error |
SphericalHankelH1[n, z] == Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (1 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.54#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(-1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}} | Error |
SphericalHankelH2[n, z] == Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 +)}, GenerateConditions->None] |
Error | Failure | - | Error |
| 10.56.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{\sqrt{z^{2}-2zt}}}{z} = \frac{\cos@@{z}}{z}+\sum_{n=1}^{\infty}\frac{t^{n}}{n!}\sphBesselJ{n-1}@{z}} | Error |
Divide[Cos[Sqrt[(z)^(2)- 2*z*t]],z] == Divide[Cos[z],z]+ Sum[Divide[(t)^(n),(n)!]*SphericalBesselJ[n - 1, z], {n, 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [42 / 42]
{Plus[Complex[-1.0653161526495918, 0.32810386977400907], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-1.8246723112251149, 0.13108435615091096], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.56.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cosh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\cosh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{1}{n-1}@{z}} | Error |
Divide[Cosh[Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Cosh[z],z]+ Sum[Divide[(I*t)^(n),(n)!]*Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [42 / 42]
{Plus[Complex[-0.13108435615091052, -1.8246723112251153], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.022834987510423566, -1.7127448295681993], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.56.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sinh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\sinh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{2}{n-1}@{z}} | Error |
Divide[Sinh[Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Sinh[z],z]+ Sum[Divide[(I*t)^(n),(n)!]*Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [42 / 42]
{Plus[Complex[-0.12983798012989667, -2.1935922908985273], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-1.4886830119296848, -1.839102010336905], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.57.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}'@{(n+\tfrac{1}{2})z} = \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}\BesselJ{n+\frac{1}{2}}'@{(n+\tfrac{1}{2})z}-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}\BesselJ{n+\frac{1}{2}}@{(n+\tfrac{1}{2})z}} | Error |
D[SphericalBesselJ[n, (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}] == Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[1,2])]*D[BesselJ[n +Divide[1,2], (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}]-Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[3,2])]*BesselJ[n +Divide[1,2], (n +Divide[1,2])* z] |
Error | Failure | - | Failed [21 / 21]
{Plus[Complex[0.14653389603833195, -0.029869009956249915], Times[Complex[-0.988457695936884, 0.2648564413786163], D[Complex[0.36567703182522004, 0.24184221354059504] <- {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], D[Complex[0.425509744388485, 0.14219887983348967], {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.06710374092328811, 0.007963502819859997], Times[Complex[-0.7656560389588212, 0.20515691731902835], D[Complex[0.2637838125883578, 0.3348231997381719] <- {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], D[Complex[0.27065896459303473, 0.20224233103375913], {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.60.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{w}}{w} = -\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselY{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Divide[Cos[w],w] == - Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselY[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [300 / 300]
{Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.60.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{w}}{w} = \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselJ{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Divide[Sin[w],w] == Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselJ[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [300 / 300]
{Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.60.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{e^{-w}}{w} = \frac{2}{\pi}\sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{v}\modsphBesselK{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Divide[Exp[- w],w] == Divide[2,Pi]*Sum[(2*n + 1)* Sqrt[Divide[Pi, v]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*Sqrt[1/2 Pi /u] BesselK[n + 1/2, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 10.60.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{iz\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)i^{n}\sphBesselJ{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Exp[I*z*Cos[\[Alpha]]] == Sum[(2*n + 1)* (I)^(n)* SphericalBesselJ[n, z]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [21 / 21]
{Plus[Complex[0.9634389243184156, 0.05909441627762202], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Plus[Complex[0.46738148067268087, 0.44423123280344756], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.60.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Exp[z*Cos[\[Alpha]]] == Sum[(2*n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [21 / 21]
{Plus[Complex[1.0625106169893304, 0.037595191618525974], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Plus[Complex[1.935725445820811, 0.9084451535292719], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.60.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}} | Error |
Exp[- z*Cos[\[Alpha]]] == Sum[(- 1)^(n)*(2*n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [21 / 21]
{Plus[Complex[0.939990215282077, -0.03326000860415312], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Plus[Complex[0.4233587200353881, -0.19868425982147583], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.60.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{z\sin@@{\alpha}} = \sum_{n=0}^{\infty}(4n+1)\frac{(2n)!}{2^{2n}(n!)^{2}}\sphBesselJ{2n}@{z}\assLegendreP[]{2n}@{\cos@@{\alpha}}} | Error |
BesselJ[0, z*Sin[\[Alpha]]] == Sum[(4*n + 1)*Divide[(2*n)!,(2)^(2*n)*((n)!)^(2)]*SphericalBesselJ[2*n, z]*LegendreP[2*n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [21 / 21]
{Plus[Complex[0.8683151459050518, -0.20203213835937428], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.0707372016677029], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}Plus[Complex[0.9708614168197589, -0.04904886793011446], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.8775825618903728], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} |
| 10.60.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\sphBesselJ{n}^{2}@{z} = \frac{\sinint@{2z}}{2z}} | Error |
Sum[(SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[SinIntegral[2*z],2*z] |
Error | Successful | - | Successful [Tested: 7] |
| 10.60.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}^{2}@{z} = 1} | Error |
Sum[(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == 1 |
Error | Failure | - | Failed [7 / 7]
{Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.60.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\sphBesselJ{n}^{2}@{z} = \frac{\sin@{2z}}{2z}} | Error |
Sum[(- 1)^(n)*(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[Sin[2*z],2*z] |
Error | Failure | - | Failed [7 / 7]
{Plus[Complex[-0.6123335037567501, 0.46246896224791606], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-1.2536290109103816, -0.6921871649112455], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \BesselJ{\nu}@{xe^{3\pi i/4}}} | KelvinBer(nu, x)+ I*KelvinBei(nu, x) = BesselJ(nu, x*exp(3*Pi*I/ 4)) |
KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x] == BesselJ[\[Nu], x*Exp[3*Pi*I/ 4]] |
Successful | Failure | Skip - symbolical successful subtest | Successful [Tested: 30] |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{xe^{3\pi i/4}} = e^{\nu\pi i}\BesselJ{\nu}@{xe^{-\pi i/4}}} | BesselJ(nu, x*exp(3*Pi*I/ 4)) = exp(nu*Pi*I)*BesselJ(nu, x*exp(- Pi*I/ 4)) |
BesselJ[\[Nu], x*Exp[3*Pi*I/ 4]] == Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], x*Exp[- Pi*I/ 4]] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\nu\pi i}\BesselJ{\nu}@{xe^{-\pi i/4}} = e^{\nu\pi i/2}\modBesselI{\nu}@{xe^{\pi i/4}}} | exp(nu*Pi*I)*BesselJ(nu, x*exp(- Pi*I/ 4)) = exp(nu*Pi*I/ 2)*BesselI(nu, x*exp(Pi*I/ 4)) |
Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], x*Exp[- Pi*I/ 4]] == Exp[\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[Pi*I/ 4]] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\nu\pi i/2}\modBesselI{\nu}@{xe^{\pi i/4}} = e^{3\nu\pi i/2}\modBesselI{\nu}@{xe^{-3\pi i/4}}} | exp(nu*Pi*I/ 2)*BesselI(nu, x*exp(Pi*I/ 4)) = exp(3*nu*Pi*I/ 2)*BesselI(nu, x*exp(- 3*Pi*I/ 4)) |
Exp[\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[Pi*I/ 4]] == Exp[3*\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[- 3*Pi*I/ 4]] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{\nu}@@{x}+i\Kelvinkei{\nu}@@{x} = e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}}} | KelvinKer(nu, x)+ I*KelvinKei(nu, x) = exp(- nu*Pi*I/ 2)*BesselK(nu, x*exp(Pi*I/ 4)) |
KelvinKer[\[Nu], x]+ I*KelvinKei[\[Nu], x] == Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], x*Exp[Pi*I/ 4]] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}} = \tfrac{1}{2}\pi i\HankelH{1}{\nu}@{xe^{3\pi i/4}}} | exp(- nu*Pi*I/ 2)*BesselK(nu, x*exp(Pi*I/ 4)) = (1)/(2)*Pi*I*HankelH1(nu, x*exp(3*Pi*I/ 4)) |
Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], x*Exp[Pi*I/ 4]] == Divide[1,2]*Pi*I*HankelH1[\[Nu], x*Exp[3*Pi*I/ 4]] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\pi i\HankelH{1}{\nu}@{xe^{3\pi i/4}} = -\tfrac{1}{2}\pi ie^{-\nu\pi i}\HankelH{2}{\nu}@{xe^{-\pi i/4}}} | (1)/(2)*Pi*I*HankelH1(nu, x*exp(3*Pi*I/ 4)) = -(1)/(2)*Pi*I*exp(- nu*Pi*I)*HankelH2(nu, x*exp(- Pi*I/ 4)) |
Divide[1,2]*Pi*I*HankelH1[\[Nu], x*Exp[3*Pi*I/ 4]] == -Divide[1,2]*Pi*I*Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], x*Exp[- Pi*I/ 4]] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}-(ix^{2}+\nu^{2})w = 0} | (x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)-(I*(x)^(2)+ (nu)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]-(I*(x)^(2)+ \[Nu]^(2))* w == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.125000000-2.948557160*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}.1249999997-1.216506352*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[1.1249999999999996, -2.948557158514987] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1249999999999996, -0.9485571585149869] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.61.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{4}\deriv[4]{w}{x}+2x^{3}\deriv[3]{w}{x}-(1+2\nu^{2})\left(x^{2}\deriv[2]{w}{x}-x\deriv{w}{x}\right)+(\nu^{4}-4\nu^{2}+x^{4})w = 0} | (x)^(4)* diff(w, [x$(4)])+ 2*(x)^(3)* diff(w, [x$(3)])-(1 + 2*(nu)^(2))*((x)^(2)* diff(w, [x$(2)])- x*diff(w, x))+((nu)^(4)- 4*(nu)^(2)+ (x)^(4))* w = 0 |
(x)^(4)* D[w, {x, 4}]+ 2*(x)^(3)* D[w, {x, 3}]-(1 + 2*\[Nu]^(2))*((x)^(2)* D[w, {x, 2}]- x*D[w, x])+(\[Nu]^(4)- 4*\[Nu]^(2)+ (x)^(4))* w == 0 |
Error | Failure | - | Skip - No test values generated |
| 10.61#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{-x} = (-1)^{n}\Kelvinber{n}@@{x}} | KelvinBer(n, - x) = (- 1)^(n)* KelvinBer(n, x) |
KelvinBer[n, - x] == (- 1)^(n)* KelvinBer[n, x] |
Successful | Failure | - | Successful [Tested: 9] |
| 10.61#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{-x} = (-1)^{n}\Kelvinbei{n}@@{x}} | KelvinBei(n, - x) = (- 1)^(n)* KelvinBei(n, x) |
KelvinBei[n, - x] == (- 1)^(n)* KelvinBei[n, x] |
Successful | Failure | - | Successful [Tested: 9] |
| 10.61#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-\nu}@@{x} = \cos@{\nu\pi}\Kelvinber{\nu}@@{x}+\sin@{\nu\pi}\Kelvinbei{\nu}@@{x}+(2/\pi)\sin@{\nu\pi}\Kelvinker{\nu}@@{x}} | KelvinBer(- nu, x) = cos(nu*Pi)*KelvinBer(nu, x)+ sin(nu*Pi)*KelvinBei(nu, x)+(2/ Pi)* sin(nu*Pi)*KelvinKer(nu, x) |
KelvinBer[- \[Nu], x] == Cos[\[Nu]*Pi]*KelvinBer[\[Nu], x]+ Sin[\[Nu]*Pi]*KelvinBei[\[Nu], x]+(2/ Pi)* Sin[\[Nu]*Pi]*KelvinKer[\[Nu], x] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{-\nu}@@{x} = -\sin@{\nu\pi}\Kelvinber{\nu}@@{x}+\cos@{\nu\pi}\Kelvinbei{\nu}@@{x}+(2/\pi)\sin@{\nu\pi}\Kelvinkei{\nu}@@{x}} | KelvinBei(- nu, x) = - sin(nu*Pi)*KelvinBer(nu, x)+ cos(nu*Pi)*KelvinBei(nu, x)+(2/ Pi)* sin(nu*Pi)*KelvinKei(nu, x) |
KelvinBei[- \[Nu], x] == - Sin[\[Nu]*Pi]*KelvinBer[\[Nu], x]+ Cos[\[Nu]*Pi]*KelvinBei[\[Nu], x]+(2/ Pi)* Sin[\[Nu]*Pi]*KelvinKei[\[Nu], x] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.61#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{-\nu}@@{x} = \cos@{\nu\pi}\Kelvinker{\nu}@@{x}-\sin@{\nu\pi}\Kelvinkei{\nu}@@{x}} | KelvinKer(- nu, x) = cos(nu*Pi)*KelvinKer(nu, x)- sin(nu*Pi)*KelvinKei(nu, x) |
KelvinKer[- \[Nu], x] == Cos[\[Nu]*Pi]*KelvinKer[\[Nu], x]- Sin[\[Nu]*Pi]*KelvinKei[\[Nu], x] |
Successful | Failure | - | Successful [Tested: 30] |
| 10.61#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{-\nu}@@{x} = \sin@{\nu\pi}\Kelvinker{\nu}@@{x}+\cos@{\nu\pi}\Kelvinkei{\nu}@@{x}} | KelvinKei(- nu, x) = sin(nu*Pi)*KelvinKer(nu, x)+ cos(nu*Pi)*KelvinKei(nu, x) |
KelvinKei[- \[Nu], x] == Sin[\[Nu]*Pi]*KelvinKer[\[Nu], x]+ Cos[\[Nu]*Pi]*KelvinKei[\[Nu], x] |
Successful | Failure | - | Successful [Tested: 30] |
| 10.61#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-n}@@{x} = (-1)^{n}\Kelvinber{n}@@{x},~{}\Kelvinbei{-n}@@{x}} | KelvinBer(- n, x) = (- 1)^(n)* KelvinBer(n, x),*KelvinBei(- n, x) |
KelvinBer[- n, x] == (- 1)^(n)* KelvinBer[n, x],*KelvinBei[- n, x] |
Error | Failure | - | Error |
| 10.61#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\Kelvinber{n}@@{x},~{}\Kelvinbei{-n}@@{x} = (-1)^{n}\Kelvinbei{n}@@{x}} | (- 1)^(n)* KelvinBer(n, x),*KelvinBei(- n, x) = (- 1)^(n)* KelvinBei(n, x) |
(- 1)^(n)* KelvinBer[n, x],*KelvinBei[- n, x] == (- 1)^(n)* KelvinBei[n, x] |
Error | Failure | - | Error |
| 10.61#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{-n}@@{x} = (-1)^{n}\Kelvinker{n}@@{x},~{}\Kelvinkei{-n}@@{x}} | KelvinKer(- n, x) = (- 1)^(n)* KelvinKer(n, x),*KelvinKei(- n, x) |
KelvinKer[- n, x] == (- 1)^(n)* KelvinKer[n, x],*KelvinKei[- n, x] |
Error | Failure | - | Error |
| 10.61#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\Kelvinker{n}@@{x},~{}\Kelvinkei{-n}@@{x} = (-1)^{n}\Kelvinkei{n}@@{x}} | (- 1)^(n)* KelvinKer(n, x),*KelvinKei(- n, x) = (- 1)^(n)* KelvinKei(n, x) |
(- 1)^(n)* KelvinKer[n, x],*KelvinKei[- n, x] == (- 1)^(n)* KelvinKei[n, x] |
Error | Failure | - | Error |
| 10.61#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos@{x+\frac{\pi}{8}}-e^{-x}\cos@{x-\frac{\pi}{8}}\right)} | KelvinBer((1)/(2), x*sqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*cos(x +(Pi)/(8))- exp(- x)*cos(x -(Pi)/(8))) |
KelvinBer[Divide[1,2], x*Sqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Cos[x +Divide[Pi,8]]- Exp[- x]*Cos[x -Divide[Pi,8]]) |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.61#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\sin@{x+\frac{\pi}{8}}+\,e^{-x}\sin@{x-\frac{\pi}{8}}\right)} | KelvinBei((1)/(2), x*sqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*sin(x +(Pi)/(8))+ exp(- x)*sin(x -(Pi)/(8))) |
KelvinBei[Divide[1,2], x*Sqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Sin[x +Divide[Pi,8]]+ Exp[- x]*Sin[x -Divide[Pi,8]]) |
Failure | Successful | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.61#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\sin@{x+\frac{\pi}{8}}-e^{-x}\sin@{x-\frac{\pi}{8}}\right)} | KelvinBer(-(1)/(2), x*sqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*sin(x +(Pi)/(8))- exp(- x)*sin(x -(Pi)/(8))) |
KelvinBer[-Divide[1,2], x*Sqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Sin[x +Divide[Pi,8]]- Exp[- x]*Sin[x -Divide[Pi,8]]) |
Failure | Successful | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.61#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{-\frac{1}{2}}@{x\sqrt{2}} = -\frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos@{x+\frac{\pi}{8}}+e^{-x}\cos@{x-\frac{\pi}{8}}\right)} | KelvinBei(-(1)/(2), x*sqrt(2)) = -((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*cos(x +(Pi)/(8))+ exp(- x)*cos(x -(Pi)/(8))) |
KelvinBei[-Divide[1,2], x*Sqrt[2]] == -Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(Exp[x]*Cos[x +Divide[Pi,8]]+ Exp[- x]*Cos[x -Divide[Pi,8]]) |
Failure | Successful | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.61.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{\frac{1}{2}}@{x\sqrt{2}} = \Kelvinkei{-\frac{1}{2}}@{x\sqrt{2}}} | KelvinKer((1)/(2), x*sqrt(2)) = KelvinKei(-(1)/(2), x*sqrt(2)) |
KelvinKer[Divide[1,2], x*Sqrt[2]] == KelvinKei[-Divide[1,2], x*Sqrt[2]] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 10.61.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{-\frac{1}{2}}@{x\sqrt{2}} = -2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\sin@{x-\frac{\pi}{8}}} | KelvinKei(-(1)/(2), x*sqrt(2)) = - (2)^(-(3)/(4))*sqrt((Pi)/(x))*exp(- x)*sin(x -(Pi)/(8)) |
KelvinKei[-Divide[1,2], x*Sqrt[2]] == - (2)^(-Divide[3,4])*Sqrt[Divide[Pi,x]]*Exp[- x]*Sin[x -Divide[Pi,8]] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.61.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{\frac{1}{2}}@{x\sqrt{2}} = -\Kelvinker{-\frac{1}{2}}@{x\sqrt{2}}} | KelvinKei((1)/(2), x*sqrt(2)) = - KelvinKer(-(1)/(2), x*sqrt(2)) |
KelvinKei[Divide[1,2], x*Sqrt[2]] == - KelvinKer[-Divide[1,2], x*Sqrt[2]] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 10.61.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\Kelvinker{-\frac{1}{2}}@{x\sqrt{2}} = -2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\cos@{x-\frac{\pi}{8}}} | - KelvinKer(-(1)/(2), x*sqrt(2)) = - (2)^(-(3)/(4))*sqrt((Pi)/(x))*exp(- x)*cos(x -(Pi)/(8)) |
- KelvinKer[-Divide[1,2], x*Sqrt[2]] == - (2)^(-Divide[3,4])*Sqrt[Divide[Pi,x]]*Exp[- x]*Cos[x -Divide[Pi,8]] |
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 10.63#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{\nu-1}(x)+f_{\nu+1}(x) = -(\nu\sqrt{2}/x)\left(f_{\nu}(x)-g_{\nu}(x)\right)} | f[nu - 1]*(x)+ f[nu + 1]*(x) = -(nu*sqrt(2)/ x)*(f[nu]*(x)- g[nu]*(x)) |
Subscript[f, \[Nu]- 1]*(x)+ Subscript[f, \[Nu]+ 1]*(x) == -(\[Nu]*Sqrt[2]/ x)*(Subscript[f, \[Nu]]*(x)- Subscript[g, \[Nu]]*(x)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.63#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinber{}'@@{x} = \Kelvinber{1}@@{x}+\Kelvinbei{1}@@{x}} | diff( KelvinBer(, x), x$(1) ) = KelvinBer(1, x)+ KelvinBei(1, x) |
D[KelvinBer[, x], {x, 1}] == KelvinBer[1, x]+ KelvinBei[1, x] |
Error | Failure | - | Failed [3 / 3]
{Plus[0.297000428957679, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 1.5]], KelvinBei[Plus[1.0, Null], 1.5], Times[-1.0, KelvinBer[Plus[-1.0, Null], 1.5]], KelvinBer[Plus[1.0, Null], 1.5]]]] <- {Rule[x, 1.5]}Plus[0.011047944038096752, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 0.5]], KelvinBei[Plus[1.0, Null], 0.5], Times[-1.0, KelvinBer[Plus[-1.0, Null], 0.5]], KelvinBer[Plus[1.0, Null], 0.5]]]] <- {Rule[x, 0.5]} |
| 10.63#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinbei{}'@@{x} = -\Kelvinber{1}x+\Kelvinbei{1}x} | diff( KelvinBei(, x), x$(1) ) = - KelvinBer(1, x)+ KelvinBei(1, x) |
D[KelvinBei[, x], {x, 1}] == - KelvinBer[1, x]+ KelvinBei[1, x] |
Error | Failure | - | Failed [3 / 3]
{Plus[-1.0327304069618592, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 1.5]], KelvinBei[Plus[1.0, Null], 1.5], KelvinBer[Plus[-1.0, Null], 1.5], Times[-1.0, KelvinBer[Plus[1.0, Null], 1.5]]]]] <- {Rule[x, 1.5]}Plus[-0.35343830347212746, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 0.5]], KelvinBei[Plus[1.0, Null], 0.5], KelvinBer[Plus[-1.0, Null], 0.5], Times[-1.0, KelvinBer[Plus[1.0, Null], 0.5]]]]] <- {Rule[x, 0.5]} |
| 10.63#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinker{}'@@{x} = \Kelvinker{1}x+\Kelvinkei{1}x} | diff( KelvinKer(, x), x$(1) ) = KelvinKer(1, x)+ KelvinKei(1, x) |
D[KelvinKer[, x], {x, 1}] == KelvinKer[1, x]+ KelvinKei[1, x] |
Error | Failure | - | Failed [3 / 3]
{Plus[0.4160356041812476, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 1.5]], KelvinKei[Plus[1.0, Null], 1.5], Times[-1.0, KelvinKer[Plus[-1.0, Null], 1.5]], KelvinKer[Plus[1.0, Null], 1.5]]]] <- {Rule[x, 1.5]}Plus[2.5735854919446126, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 0.5]], KelvinKei[Plus[1.0, Null], 0.5], Times[-1.0, KelvinKer[Plus[-1.0, Null], 0.5]], KelvinKer[Plus[1.0, Null], 0.5]]]] <- {Rule[x, 0.5]} |
| 10.63#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinkei{}'@@{x} = -\Kelvinker{1}x+\Kelvinkei{1}x} | diff( KelvinKei(, x), x$(1) ) = - KelvinKer(1, x)+ KelvinKei(1, x) |
D[KelvinKei[, x], {x, 1}] == - KelvinKer[1, x]+ KelvinKei[1, x] |
Error | Failure | - | Failed [3 / 3]
{Plus[-0.418052966151267, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 1.5]], KelvinKei[Plus[1.0, Null], 1.5], KelvinKer[Plus[-1.0, Null], 1.5], Times[-1.0, KelvinKer[Plus[1.0, Null], 1.5]]]]] <- {Rule[x, 1.5]}Plus[-0.47122132111956727, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 0.5]], KelvinKei[Plus[1.0, Null], 0.5], KelvinKer[Plus[-1.0, Null], 0.5], Times[-1.0, KelvinKer[Plus[1.0, Null], 0.5]]]]] <- {Rule[x, 0.5]} |
| 10.63#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu+1} = p_{\nu-1}-(4\nu/x)r_{\nu}} | p[nu + 1] = p[nu - 1]-(4*nu/ x)* r[nu] |
Subscript[p, \[Nu]+ 1] == Subscript[p, \[Nu]- 1]-(4*\[Nu]/ x)* Subscript[r, \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.63#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{\nu+1} = -(\nu/x)p_{\nu}+r_{\nu}} | q[nu + 1] = -(nu/ x)* p[nu]+ r[nu] |
Subscript[q, \[Nu]+ 1] == -(\[Nu]/ x)* Subscript[p, \[Nu]]+ Subscript[r, \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.63#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{\nu+1} = -((\nu+1)/x)p_{\nu+1}+q_{\nu}} | r[nu + 1] = -((nu + 1)/ x)* p[nu + 1]+ q[nu] |
Subscript[r, \[Nu]+ 1] == -((\[Nu]+ 1)/ x)* Subscript[p, \[Nu]+ 1]+ Subscript[q, \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.63#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{\nu} = \tfrac{1}{2}p_{\nu+1}+\tfrac{1}{2}p_{\nu-1}-(\nu^{2}/x^{2})p_{\nu}} | s[nu] = (1)/(2)*p[nu + 1]+(1)/(2)*p[nu - 1]-((nu)^(2)/ (x)^(2))* p[nu] |
Subscript[s, \[Nu]] == Divide[1,2]*Subscript[p, \[Nu]+ 1]+Divide[1,2]*Subscript[p, \[Nu]- 1]-(\[Nu]^(2)/ (x)^(2))* Subscript[p, \[Nu]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.63.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu}s_{\nu} = r_{\nu}^{2}+q_{\nu}^{2}} | p[nu]*s[nu] = (r[nu])^(2)+ (q[nu])^(2) |
Subscript[p, \[Nu]]*Subscript[s, \[Nu]] == (Subscript[r, \[Nu]])^(2)+ (Subscript[q, \[Nu]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 10.64.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}} | KelvinBer(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi) |
KelvinBer[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 9] | Skipped - Because timed out |
| 10.64.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}} | KelvinBei(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi) |
KelvinBei[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 9] | Skipped - Because timed out |
| 10.65#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\cos@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}} | KelvinBer(nu, x) = ((1)/(2)*x)^(nu)* sum((cos((3)/(4)*nu*Pi +(1)/(2)*k*Pi))/(factorial(k)*GAMMA(nu + k + 1))*((1)/(4)*(x)^(2))^(k), k = 0..infinity) |
KelvinBer[\[Nu], x] == (Divide[1,2]*x)^\[Nu]* Sum[Divide[Cos[Divide[3,4]*\[Nu]*Pi +Divide[1,2]*k*Pi],(k)!*Gamma[\[Nu]+ k + 1]]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.65#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\sin@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}} | KelvinBei(nu, x) = ((1)/(2)*x)^(nu)* sum((sin((3)/(4)*nu*Pi +(1)/(2)*k*Pi))/(factorial(k)*GAMMA(nu + k + 1))*((1)/(4)*(x)^(2))^(k), k = 0..infinity) |
KelvinBei[\[Nu], x] == (Divide[1,2]*x)^\[Nu]* Sum[Divide[Sin[Divide[3,4]*\[Nu]*Pi +Divide[1,2]*k*Pi],(k)!*Gamma[\[Nu]+ k + 1]]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Successful [Tested: 30] | Successful [Tested: 30] |
| 10.65#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{}@@{x} = 1-\frac{(\frac{1}{4}x^{2})^{2}}{(2!)^{2}}+\frac{(\frac{1}{4}x^{2})^{4}}{(4!)^{2}}-\dotsb} | KelvinBer(, x) = 1 -(((1)/(4)*(x)^(2))^(2))/((factorial(2))^(2))+(((1)/(4)*(x)^(2))^(4))/((factorial(4))^(2))- .. |
KelvinBer[, x] == 1 -Divide[(Divide[1,4]*(x)^(2))^(2),((2)!)^(2)]+Divide[(Divide[1,4]*(x)^(2))^(4),((4)!)^(2)]- \[Ellipsis] |
Error | Failure | - | Failed [3 / 3]
{Plus[-0.921072244644165, …, KelvinBer[Null, 1.5]] <- {Rule[x, 1.5]}Plus[-0.9990234639909532, …, KelvinBer[Null, 0.5]] <- {Rule[x, 0.5]} |
| 10.65#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{}@@{x} = \tfrac{1}{4}x^{2}-\frac{(\frac{1}{4}x^{2})^{3}}{(3!)^{2}}+\frac{(\frac{1}{4}x^{2})^{5}}{(5!)^{2}}-\dotsi} | KelvinBei(, x) = (1)/(4)*(x)^(2)-(((1)/(4)*(x)^(2))^(3))/((factorial(3))^(2))+(((1)/(4)*(x)^(2))^(5))/((factorial(5))^(2))- .. |
KelvinBei[, x] == Divide[1,4]*(x)^(2)-Divide[(Divide[1,4]*(x)^(2))^(3),((3)!)^(2)]+Divide[(Divide[1,4]*(x)^(2))^(5),((5)!)^(2)]- \[Ellipsis] |
Error | Failure | - | Failed [3 / 3]
{Plus[-0.5575600630044937, …, KelvinBei[Null, 1.5]] <- {Rule[x, 1.5]}Plus[-0.06249321838219961, …, KelvinBei[Null, 0.5]] <- {Rule[x, 0.5]} |
| 10.65#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinbei{}@@{x}-\tfrac{1}{4}\pi\Kelvinber{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+2}}{((2k+1)!)^{2}}(\tfrac{1}{4}x^{2})^{2k+1}} | KelvinBer(, x)+ sum((- 1)^(k)*(Psi(2*k + 2))/((factorial(2*k + 1))^(2))*((1)/(4)*(x)^(2))^(2*k + 1), k = 0..infinity) |
KelvinBer[, x]+ Sum[(- 1)^(k)*Divide[PolyGamma[2*k + 2],((2*k + 1)!)^(2)]*(Divide[1,4]*(x)^(2))^(2*k + 1), {k, 0, Infinity}, GenerateConditions->None] |
Error | Failure | - | Failed [3 / 3]
{Plus[-0.23161280473545226, Times[-1.0, KelvinBer[Null, 1.5]], KelvinKei[Null, 1.5]] <- {Rule[x, 1.5]}Plus[-0.02641550246351669, Times[-1.0, KelvinBer[Null, 0.5]], KelvinKei[Null, 0.5]] <- {Rule[x, 0.5]} |
| 10.65.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x} = (\tfrac{1}{2}x)^{2\nu}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | (KelvinBer(nu, x))^(2)+ (KelvinBei(nu, x))^(2) = ((1)/(2)*x)^(2*nu)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 1))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
(KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2) == (Divide[1,2]*x)^(2*\[Nu])* Sum[Divide[1,Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 1]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Successful | Successful | - | Successful [Tested: 30] |
| 10.65.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x} = (\tfrac{1}{2}x)^{2\nu+1}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+2}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | KelvinBer(nu, x)*diff( KelvinBei(nu, x), x$(1) )- diff( KelvinBer(nu, x), x$(1) )*KelvinBei(nu, x) = ((1)/(2)*x)^(2*nu + 1)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 2))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
KelvinBer[\[Nu], x]*D[KelvinBei[\[Nu], x], {x, 1}]- D[KelvinBer[\[Nu], x], {x, 1}]*KelvinBei[\[Nu], x] == (Divide[1,2]*x)^(2*\[Nu]+ 1)* Sum[Divide[1,Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 2]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Successful | Failed [21 / 30] 21/30]: [[.7271930e-3+.45983036e-2*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}-.41528503e-2+.322695404e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 2} |
Failed [3 / 30]
{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]} |
| 10.65.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}\Kelvinber{\nu}'@@{x}+\Kelvinbei{\nu}@@{x}\Kelvinbei{\nu}'@@{x} = \tfrac{1}{2}(\tfrac{1}{2}x)^{2\nu-1}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | KelvinBer(nu, x)*diff( KelvinBer(nu, x), x$(1) )+ KelvinBei(nu, x)*diff( KelvinBei(nu, x), x$(1) ) = (1)/(2)*((1)/(2)*x)^(2*nu - 1)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
KelvinBer[\[Nu], x]*D[KelvinBer[\[Nu], x], {x, 1}]+ KelvinBei[\[Nu], x]*D[KelvinBei[\[Nu], x], {x, 1}] == Divide[1,2]*(Divide[1,2]*x)^(2*\[Nu]- 1)* Sum[Divide[1,Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Successful | Failed [25 / 30] 25/30]: [[.71978298e-2-.3037583875e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}.607273780e-1-.1071579728*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 2} |
Failed [3 / 30]
{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]} |
| 10.65.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\Kelvinber{\nu}'@@{x}\right)^{2}+\left(\Kelvinbei{\nu}'@@{x}\right)^{2} = (\tfrac{1}{2}x)^{2\nu-2}\sum_{k=0}^{\infty}\frac{2k^{2}+2\nu k+\frac{1}{4}\nu^{2}}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}} | (diff( KelvinBer(nu, x), x$(1) ))^(2)+(diff( KelvinBei(nu, x), x$(1) ))^(2) = ((1)/(2)*x)^(2*nu - 2)* sum((2*(k)^(2)+ 2*nu*k +(1)/(4)*(nu)^(2))/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 1))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity) |
(D[KelvinBer[\[Nu], x], {x, 1}])^(2)+(D[KelvinBei[\[Nu], x], {x, 1}])^(2) == (Divide[1,2]*x)^(2*\[Nu]- 2)* Sum[Divide[2*(k)^(2)+ 2*\[Nu]*k +Divide[1,4]*\[Nu]^(2),Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 1]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Successful | Failed [3 / 30] 3/30]: [[Float(undefined)+Float(undefined)*I <- {nu = -2, x = 3/2}Float(undefined)+Float(undefined)*I <- {nu = -2, x = 1/2} |
Failed [3 / 30]
{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]} |
| 10.66.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!}} | KelvinBer(nu, x)+ I*KelvinBei(nu, x) = sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) |
KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x] == Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [30 / 30]
{Plus[Complex[-0.12257968900025018, 0.2735107661041647], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.3467793075651209, -0.08562995402477025], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.66.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}\modBesselI{\nu+k}@{x}}{2^{k/2}k!}} | sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) = sum((exp((3*nu + 3*k)* Pi*I/ 4)*(x)^(k)* BesselI(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) |
Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None] == Sum[Divide[Exp[(3*\[Nu]+ 3*k)* Pi*I/ 4]*(x)^(k)* BesselI[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [30 / 30]
{Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, k]], Pi]], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Times[3, k]], Pi]], BesselI[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.66#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k}@{x}\modBesselI{2k}@{x}} | KelvinBer(n, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k, x)*BesselI(2*k, x), k = - infinity..infinity) |
KelvinBer[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k, x]*BesselI[2*k, x], {k, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 9] | Skipped - Because timed out |
| 10.66#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k+1}@{x}\modBesselI{2k+1}@{x}} | KelvinBei(n, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k + 1, x)*BesselI(2*k + 1, x), k = - infinity..infinity) |
KelvinBei[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k + 1, x]*BesselI[2*k + 1, x], {k, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Error | Successful [Tested: 9] | Skipped - Because timed out |
| 10.68#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{\nu}@{x} = (\Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x})^{\ifrac{1}{2}}} | Error |
Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2))^(Divide[1,2]) |
Error | Successful | - | Successful [Tested: 30] |
| 10.68#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{\nu}@{x} = (\Kelvinker{\nu}^{2}@@{x}+\Kelvinkei{\nu}^{2}@@{x})^{\ifrac{1}{2}}} | Error |
Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((KelvinKer[\[Nu], x])^(2)+ (KelvinKei[\[Nu], x])^(2))^(Divide[1,2]) |
Error | Successful | - | Successful [Tested: 30] |
| 10.68#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{-n}@{x} = \HankelmodM{n}@{x}} | Error |
Sqrt[KelvinBer[- n, x]^2 + KelvinBei[- n, x]^2] == Sqrt[KelvinBer[n, x]^2 + KelvinBei[n, x]^2] |
Error | Failure | - | Successful [Tested: 9] |
| 10.68#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{-\nu}@{x} = \HankelmodderivN{\nu}@{x}} | Error |
Sqrt[KelvinKer[- \[Nu], x]^2 + KelvinKei[- \[Nu], x]^2] == Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] |
Error | Failure | - | Successful [Tested: 30] |
| 10.71.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x^{1+\nu}f_{\nu}\diff{x} = -\frac{x^{1+\nu}}{\sqrt{2}}(f_{\nu+1}-g_{\nu+1})} | int((x)^(1 + nu)* f[nu], x) = -((x)^(1 + nu))/(sqrt(2))*(f[nu + 1]- g[nu + 1]) |
Integrate[(x)^(1 + \[Nu])* Subscript[f, \[Nu]], x, GenerateConditions->None] == -Divide[(x)^(1 + \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]+ 1]- Subscript[g, \[Nu]+ 1]) |
Failure | Failure | Failed [300 / 300] 300/300]: [[.9346151411+.5776724966*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[1+nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = 1/2*3^(1/2)+1/2*I}3.061934630+.4518721345*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[1+nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.9346151408625077, 0.5776724967688012] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.061934629891139, 0.45187213490403344] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.71.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x^{1-\nu}f_{\nu}\diff{x} = \frac{x^{1-\nu}}{\sqrt{2}}(f_{\nu-1}-g_{\nu-1})} | int((x)^(1 - nu)* f[nu], x) = ((x)^(1 - nu))/(sqrt(2))*(f[nu - 1]- g[nu - 1]) |
Integrate[(x)^(1 - \[Nu])* Subscript[f, \[Nu]], x, GenerateConditions->None] == Divide[(x)^(1 - \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]- 1]- Subscript[g, \[Nu]- 1]) |
Failure | Failure | Failed [300 / 300] 300/300]: [[.9470105611+.8580421171*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu-1] = 1/2*3^(1/2)+1/2*I}.30703090e-2+1.331056152*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu-1] = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.9470105613079453, 0.8580421172974921] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.0030703089818392426, 1.3310561520338196] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 10.71.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int xf_{\nu}g_{\nu}\diff{x} = \tfrac{1}{4}x^{2}\left(2f_{\nu}g_{\nu}-f_{\nu-1}g_{\nu+1}-f_{\nu+1}g_{\nu-1}\right)} | int(x*f[nu]*g[nu], x) = (1)/(4)*(x)^(2)*(2*f[nu]*g[nu]- f[nu - 1]*g[nu + 1]- f[nu + 1]*g[nu - 1]) |
Integrate[x*Subscript[f, \[Nu]]*Subscript[g, \[Nu]], x, GenerateConditions->None] == Divide[1,4]*(x)^(2)*(2*Subscript[f, \[Nu]]*Subscript[g, \[Nu]]- Subscript[f, \[Nu]- 1]*Subscript[g, \[Nu]+ 1]- Subscript[f, \[Nu]+ 1]*Subscript[g, \[Nu]- 1]) |
Failure | Failure | Failed [270 / 300] 270/300]: [[.5625000004+.9742785795*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[1+nu] = 1/2*3^(1/2)+1/2*I, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = 1/2*3^(1/2)+1/2*I, g[nu-1] = 1/2*3^(1/2)+1/2*I}-.2058892896+.7683892900*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[1+nu] = 1/2*3^(1/2)+1/2*I, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = 1/2*3^(1/2)+1/2*I, g[nu-1] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 10.71.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x(f_{\nu}^{2}-g_{\nu}^{2})\diff{x} = \tfrac{1}{2}x^{2}\left(f_{\nu}^{2}-f_{\nu-1}f_{\nu+1}-g_{\nu}^{2}+g_{\nu-1}g_{\nu+1}\right)} | int(x*(f(f[nu])^(2)- g(g[nu])^(2)), x) = (f(f[nu])^(2)- f[nu - 1]*f[nu + 1]- g(g[nu])^(2)+ g[nu - 1]*g[nu + 1]) |
Integrate[x*(f(Subscript[f, \[Nu]])^(2)- g(Subscript[g, \[Nu]])^(2)), x, GenerateConditions->None] == (f(Subscript[f, \[Nu]])^(2)- Subscript[f, \[Nu]- 1]*Subscript[f, \[Nu]+ 1]- g(Subscript[g, \[Nu]])^(2)+ Subscript[g, \[Nu]- 1]*Subscript[g, \[Nu]+ 1]) |
Failure | Failure | Error | Error |
| 10.71#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x\HankelmodM{\nu}^{2}@{x}\diff{x} = x(\Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x})} | Error |
Integrate[x*(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x*(KelvinBer[\[Nu], x]*D[KelvinBei[\[Nu], x], {x, 1}]- D[KelvinBer[\[Nu], x], {x, 1}]*KelvinBei[\[Nu], x]) |
Error | Successful | - | Successful [Tested: 30] |
| 10.71#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x\HankelmodderivN{\nu}^{2}@{x}\diff{x} = x(\Kelvinker{\nu}@@{x}\Kelvinkei{\nu}'@@{x}-\Kelvinker{\nu}'@@{x}\Kelvinkei{\nu}@@{x})} | Error |
Integrate[x*(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x*(KelvinKer[\[Nu], x]*D[KelvinKei[\[Nu], x], {x, 1}]- D[KelvinKer[\[Nu], x], {x, 1}]*KelvinKei[\[Nu], x]) |
Error | Successful | - | Successful [Tested: 30] |
| 10.73.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{r}\pderiv{}{r}\left(r\pderiv{V}{r}\right)+\frac{1}{r^{2}}\pderiv[2]{V}{\phi}+\pderiv[2]{V}{z} = 0} | (1)/(r)*diff((r*diff(V, r))+(1)/((r)^(2))*diff(V, [phi$(2)]), r)+ diff(V, [z$(2)]) = 0 |
Divide[1,r]*D[(r*D[V, r])+Divide[1,(r)^(2)]*D[V, {\[Phi], 2}], r]+ D[V, {z, 2}] == 0 |
Successful | Successful | - | Successful [Tested: 300] |