Results of Bessel Functions I
This is the first half of the chapter Bessel Functions. It from Section 10.2 to 10.32. For Section 10.33 to 10.73 go to Bessel Functions II.
| 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 |