Results of Error Functions, Dawson’s and Fresnel Integrals

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DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
7.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{2}{\sqrt{\pi}}\int_{0}^{z}e^{-t^{2}}\diff{t}} erf(z) = (2)/(sqrt(Pi))*int(exp(- (t)^(2)), t = 0..z) Erf[z] == Divide[2,Sqrt[Pi]]*Integrate[Exp[- (t)^(2)], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{2}{\sqrt{\pi}}\int_{z}^{\infty}e^{-t^{2}}\diff{t}} erfc(z) = (2)/(sqrt(Pi))*int(exp(- (t)^(2)), t = z..infinity) Erfc[z] == Divide[2,Sqrt[Pi]]*Integrate[Exp[- (t)^(2)], {t, z, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\sqrt{\pi}}\int_{z}^{\infty}e^{-t^{2}}\diff{t} = 1-\erf@@{z}} (2)/(sqrt(Pi))*int(exp(- (t)^(2)), t = z..infinity) = 1 - erf(z) Divide[2,Sqrt[Pi]]*Integrate[Exp[- (t)^(2)], {t, z, Infinity}, GenerateConditions->None] == 1 - Erf[z] Successful Successful - Successful [Tested: 7]
7.2.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z^{2}}\left(1+\frac{2i}{\sqrt{\pi}}\int_{0}^{z}e^{t^{2}}\diff{t}\right) = e^{-z^{2}}\erfc@{-iz}} exp(- (z)^(2))*(1 +(2*I)/(sqrt(Pi))*int(exp((t)^(2)), t = 0..z)) = exp(- (z)^(2))*erfc(- I*z) Exp[- (z)^(2)]*(1 +Divide[2*I,Sqrt[Pi]]*Integrate[Exp[(t)^(2)], {t, 0, z}, GenerateConditions->None]) == Exp[- (z)^(2)]*Erfc[- I*z] Successful Successful - Successful [Tested: 7]
7.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to\infty}\erf@@{z} = 1} limit(erf(z), z = infinity) = 1 Limit[Erf[z], z -> Infinity, GenerateConditions->None] == 1 Successful Successful - Successful [Tested: 1]
7.2#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to\infty}\erfc@@{z} = 0} limit(erfc(z), z = infinity) = 0 Limit[Erfc[z], z -> Infinity, GenerateConditions->None] == 0 Successful Successful - Successful [Tested: 1]
7.2.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \DawsonsintF@{z} = e^{-z^{2}}\int_{0}^{z}e^{t^{2}}\diff{t}} dawson(z) = exp(- (z)^(2))*int(exp((t)^(2)), t = 0..z) DawsonF[z] == Exp[- (z)^(2)]*Integrate[Exp[(t)^(2)], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.2.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \FresnelintF@{z} = \int_{z}^{\infty}e^{\tfrac{1}{2}\pi\iunit t^{2}}\diff{t}} Error (1+I)/2-FresnelC[z]-I*FresnelS[z] == Integrate[Exp[Divide[1,2]*Pi*I*(t)^(2)], {t, z, Infinity}, GenerateConditions->None] Missing Macro Error Failure -
Failed [2 / 7]
{Complex[-0.17236809983536389, -1.1316008349021112] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[0.17236809983536283, 1.1316008349021118] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
7.2.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = \int_{0}^{z}\cos@{\tfrac{1}{2}\pi t^{2}}\diff{t}} FresnelC(z) = int(cos((1)/(2)*Pi*(t)^(2)), t = 0..z) FresnelC[z] == Integrate[Cos[Divide[1,2]*Pi*(t)^(2)], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.2.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = \int_{0}^{z}\sin@{\tfrac{1}{2}\pi t^{2}}\diff{t}} FresnelS(z) = int(sin((1)/(2)*Pi*(t)^(2)), t = 0..z) FresnelS[z] == Integrate[Sin[Divide[1,2]*Pi*(t)^(2)], {t, 0, z}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.2#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to\infty}\Fresnelcosint@{x} = \tfrac{1}{2}} limit(FresnelC(x), x = infinity) = (1)/(2) Limit[FresnelC[x], x -> Infinity, GenerateConditions->None] == Divide[1,2] Successful Successful - Successful [Tested: 1]
7.2#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{x\to\infty}\Fresnelsinint@{x} = \tfrac{1}{2}} limit(FresnelS(x), x = infinity) = (1)/(2) Limit[FresnelS[x], x -> Infinity, GenerateConditions->None] == Divide[1,2] Successful Successful - Successful [Tested: 1]
7.2.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{z} = \left(\tfrac{1}{2}-\Fresnelsinint@{z}\right)\cos@{\tfrac{1}{2}\pi z^{2}}-\left(\tfrac{1}{2}-\Fresnelcosint@{z}\right)\sin@{\tfrac{1}{2}\pi z^{2}}} Fresnelf(z) = ((1)/(2)- FresnelS(z))* cos((1)/(2)*Pi*(z)^(2))-((1)/(2)- FresnelC(z))* sin((1)/(2)*Pi*(z)^(2)) FresnelF[z] == (Divide[1,2]- FresnelS[z])* Cos[Divide[1,2]*Pi*(z)^(2)]-(Divide[1,2]- FresnelC[z])* Sin[Divide[1,2]*Pi*(z)^(2)] Successful Successful - Successful [Tested: 7]
7.2.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{z} = \left(\tfrac{1}{2}-\Fresnelcosint@{z}\right)\cos@{\tfrac{1}{2}\pi z^{2}}+\left(\tfrac{1}{2}-\Fresnelsinint@{z}\right)\sin@{\tfrac{1}{2}\pi z^{2}}} Fresnelg(z) = ((1)/(2)- FresnelC(z))* cos((1)/(2)*Pi*(z)^(2))+((1)/(2)- FresnelS(z))* sin((1)/(2)*Pi*(z)^(2)) FresnelG[z] == (Divide[1,2]- FresnelC[z])* Cos[Divide[1,2]*Pi*(z)^(2)]+(Divide[1,2]- FresnelS[z])* Sin[Divide[1,2]*Pi*(z)^(2)] Successful Successful - Successful [Tested: 7]
7.4.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@{-z} = -\erf@{z}} erf(- z) = - erf(z) Erf[- z] == - Erf[z] Successful Successful - Successful [Tested: 7]
7.4.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@{-z} = 2-\erfc@{z}} erfc(- z) = 2 - erfc(z) Erfc[- z] == 2 - Erfc[z] Successful Successful - Successful [Tested: 7]
7.4.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \DawsonsintF@{-z} = -\DawsonsintF@{z}} dawson(- z) = - dawson(z) DawsonF[- z] == - DawsonF[z] Successful Successful - Successful [Tested: 7]
7.4#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{-z} = -\Fresnelcosint@{z}} FresnelC(- z) = - FresnelC(z) FresnelC[- z] == - FresnelC[z] Successful Successful - Successful [Tested: 7]
7.4#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{-z} = -\Fresnelsinint@{z}} FresnelS(- z) = - FresnelS(z) FresnelS[- z] == - FresnelS[z] Successful Successful - Successful [Tested: 7]
7.4#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{iz} = i\Fresnelcosint@{z}} FresnelC(I*z) = I*FresnelC(z) FresnelC[I*z] == I*FresnelC[z] Successful Successful - Successful [Tested: 7]
7.4#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{iz} = -i\Fresnelsinint@{z}} FresnelS(I*z) = - I*FresnelS(z) FresnelS[I*z] == - I*FresnelS[z] Successful Successful - Successful [Tested: 7]
7.4#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z}} Fresnelf(I*z) = (1/(sqrt(2)))* exp((1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))- I*Fresnelf(z) FresnelF[I*z] == (1/(Sqrt[2]))* Exp[Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]- I*FresnelF[z] Failure Failure Successful [Tested: 7] Successful [Tested: 7]
7.4#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z}} Fresnelg(I*z) = (1/(sqrt(2)))* exp(-(1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))+ I*Fresnelg(z) FresnelG[I*z] == (1/(Sqrt[2]))* Exp[-Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]+ I*FresnelG[z] Failure Failure Successful [Tested: 7] Successful [Tested: 7]
7.4#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z}} Fresnelf(- z) = sqrt(2)*cos((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelf(z) FresnelF[- z] == Sqrt[2]*Cos[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelF[z] Successful Successful - Successful [Tested: 7]
7.4#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}} Fresnelg(- z) = sqrt(2)*sin((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelg(z) FresnelG[- z] == Sqrt[2]*Sin[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelG[z] Successful Failure - Successful [Tested: 7]
7.5.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z}+i\Fresnelsinint@{z} = \tfrac{1}{2}(1+i)-\FresnelintF@{z}} Error FresnelC[z]+ I*FresnelS[z] == Divide[1,2]*(1 + I)- (1+I)/2-FresnelC[z]-I*FresnelS[z] Missing Macro Error Failure -
Failed [7 / 7]
{Complex[1.0249430142401041, 0.8677085978643018] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.5229723981935741, 3.2881446840443265] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.5.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = \tfrac{1}{2}+\auxFresnelf@{z}\sin@{\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}\cos@{\tfrac{1}{2}\pi z^{2}}} FresnelC(z) = (1)/(2)+ Fresnelf(z)*sin((1)/(2)*Pi*(z)^(2))- Fresnelg(z)*cos((1)/(2)*Pi*(z)^(2)) FresnelC[z] == Divide[1,2]+ FresnelF[z]*Sin[Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]*Cos[Divide[1,2]*Pi*(z)^(2)] Successful Failure - Successful [Tested: 7]
7.5.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = \tfrac{1}{2}-\auxFresnelf@{z}\cos@{\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}\sin@{\tfrac{1}{2}\pi z^{2}}} FresnelS(z) = (1)/(2)- Fresnelf(z)*cos((1)/(2)*Pi*(z)^(2))- Fresnelg(z)*sin((1)/(2)*Pi*(z)^(2)) FresnelS[z] == Divide[1,2]- FresnelF[z]*Cos[Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]*Sin[Divide[1,2]*Pi*(z)^(2)] Successful Failure - Successful [Tested: 7]
7.5.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{2}\pi iz^{2}}\FresnelintF@{z} = \auxFresnelg@{z}+i\auxFresnelf@{z}} Error Exp[-Divide[1,2]*Pi*I*(z)^(2)]*(1+I)/2-FresnelC[z]-I*FresnelS[z] == FresnelG[z]+ I*FresnelF[z] Missing Macro Error Failure -
Failed [6 / 7]
{Complex[2.0955908860316255, -0.6505223669676224] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.08422623998042833, -1.3932392044453867] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.5.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+\frac{1}{2}\pi iz^{2}}(\auxFresnelg@{z}+ i\auxFresnelf@{z}) = \tfrac{1}{2}(1+ i)-(\Fresnelcosint@{z}+ i\Fresnelsinint@{z})} exp(+(1)/(2)*Pi*I*(z)^(2))*(Fresnelg(z)+ I*Fresnelf(z)) = (1)/(2)*(1 + I)-(FresnelC(z)+ I*FresnelS(z)) Exp[+Divide[1,2]*Pi*I*(z)^(2)]*(FresnelG[z]+ I*FresnelF[z]) == Divide[1,2]*(1 + I)-(FresnelC[z]+ I*FresnelS[z]) Successful Failure - Successful [Tested: 7]
7.5.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{2}\pi iz^{2}}(\auxFresnelg@{z}- i\auxFresnelf@{z}) = \tfrac{1}{2}(1- i)-(\Fresnelcosint@{z}- i\Fresnelsinint@{z})} exp(-(1)/(2)*Pi*I*(z)^(2))*(Fresnelg(z)- I*Fresnelf(z)) = (1)/(2)*(1 - I)-(FresnelC(z)- I*FresnelS(z)) Exp[-Divide[1,2]*Pi*I*(z)^(2)]*(FresnelG[z]- I*FresnelF[z]) == Divide[1,2]*(1 - I)-(FresnelC[z]- I*FresnelS[z]) Successful Failure - Successful [Tested: 7]
7.5.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z}+ i\Fresnelsinint@{z} = \tfrac{1}{2}(1+ i)\erf@@{\zeta}} FresnelC(z)+ I*FresnelS(z) = (1)/(2)*(1 + I)* erf(zeta) FresnelC[z]+ I*FresnelS[z] == Divide[1,2]*(1 + I)* Erf[\[Zeta]] Successful Successful Skip - symbolical successful subtest Successful [Tested: 7]
7.5.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z}- i\Fresnelsinint@{z} = \tfrac{1}{2}(1- i)\erf@@{\zeta}} FresnelC(z)- I*FresnelS(z) = (1)/(2)*(1 - I)* erf(zeta) FresnelC[z]- I*FresnelS[z] == Divide[1,2]*(1 - I)* Erf[\[Zeta]] Failure Failure
Failed [7 / 7]
7/7]: [[1.210218044+.7739577054*I <- {z = 1/2*3^(1/2)+1/2*I}
-2.077926642+.2509853077*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [7 / 7]
{Complex[1.210218043090013, 0.7739577062168396] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-2.0779266409543133, 0.2509853080232649] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.5.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{z}+ i\auxFresnelf@{z} = \tfrac{1}{2}(1+ i)e^{\zeta^{2}}\erfc@@{\zeta}} Fresnelg(z)+ I*Fresnelf(z) = (1)/(2)*(1 + I)* exp((zeta)^(2))*erfc(zeta) FresnelG[z]+ I*FresnelF[z] == Divide[1,2]*(1 + I)* Exp[\[Zeta]^(2)]*Erfc[\[Zeta]] Successful Failure Skip - symbolical successful subtest Successful [Tested: 7]
7.5.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{z}- i\auxFresnelf@{z} = \tfrac{1}{2}(1- i)e^{\zeta^{2}}\erfc@@{\zeta}} Fresnelg(z)- I*Fresnelf(z) = (1)/(2)*(1 - I)* exp((zeta)^(2))*erfc(zeta) FresnelG[z]- I*FresnelF[z] == Divide[1,2]*(1 - I)* Exp[\[Zeta]^(2)]*Erfc[\[Zeta]] Failure Failure
Failed [7 / 7]
7/7]: [[-.2860780540-.1977870141*I <- {z = 1/2*3^(1/2)+1/2*I}
-.1472580850-5.018337775*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [7 / 7]
{Complex[-0.2860780524436176, -0.19778701442673574] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.14725808362732817, -5.018337771876615] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.5.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\FresnelintF@{x}|^{2} = \auxFresnelf^{2}@{x}+\auxFresnelg^{2}@{x}} Error (Abs[(1+I)/2-FresnelC[x]-I*FresnelS[x]])^(2) == (FresnelF[x])^(2)+ (FresnelG[x])^(2) Missing Macro Error Failure - Successful [Tested: 3]
7.5.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\FresnelintF@{x}|^{2} = 2+\auxFresnelf^{2}@{-x}+\auxFresnelg^{2}@{-x}-2\sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi x^{2}}\auxFresnelf@{-x}-2\sqrt{2}\cos@{\tfrac{1}{4}\pi-\tfrac{1}{2}\pi x^{2}}\auxFresnelg@{-x}} Error (Abs[(1+I)/2-FresnelC[x]-I*FresnelS[x]])^(2) == 2 + (FresnelF[- x])^(2)+ (FresnelG[- x])^(2)- 2*Sqrt[2]*Cos[Divide[1,4]*Pi +Divide[1,2]*Pi*(x)^(2)]*FresnelF[- x]- 2*Sqrt[2]*Cos[Divide[1,4]*Pi -Divide[1,2]*Pi*(x)^(2)]*FresnelG[- x] Missing Macro Error Failure - Skip - No test values generated
7.6.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{2}{\sqrt{\pi}}\sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n+1}}{n!(2n+1)}} erf(z) = (2)/(sqrt(Pi))*sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(n)*(2*n + 1)), n = 0..infinity) Erf[z] == Divide[2,Sqrt[Pi]]*Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(n)!*(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.6.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{2}{\sqrt{\pi}}e^{-z^{2}}\sum_{n=0}^{\infty}\frac{2^{n}z^{2n+1}}{1\cdot 3\cdots(2n+1)}} erf(z) = (2)/(sqrt(Pi))*exp(- (z)^(2))*sum(((2)^(n)* (z)^(2*n + 1))/(1 * 3*(2*n + 1)), n = 0..infinity) Erf[z] == Divide[2,Sqrt[Pi]]*Exp[- (z)^(2)]*Sum[Divide[(2)^(n)* (z)^(2*n + 1),1 * 3*(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] Failure Failure
Failed [7 / 7]
7/7]: [[.7078919422+.2093474075*I <- {z = 1/2*3^(1/2)+1/2*I}
-.5779386350+.6643773058*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [7 / 7]
{Complex[0.7078919419896831, 0.20934740753145048] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.5779386346997313, 0.6643773053985802] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.6.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}(\frac{1}{2}\pi)^{2n}}{(2n)!(4n+1)}z^{4n+1}} FresnelC(z) = sum(((- 1)^(n)*((1)/(2)*Pi)^(2*n))/(factorial(2*n)*(4*n + 1))*(z)^(4*n + 1), n = 0..infinity) FresnelC[z] == Sum[Divide[(- 1)^(n)*(Divide[1,2]*Pi)^(2*n),(2*n)!*(4*n + 1)]*(z)^(4*n + 1), {n, 0, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.6.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = \cos@{\tfrac{1}{2}\pi z^{2}}\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n}}{1\cdot 3\cdots(4n+1)}z^{4n+1}+\sin@{\tfrac{1}{2}\pi z^{2}}\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n+1}}{1\cdot 3\cdots(4n+3)}z^{4n+3}} FresnelC(z) = cos((1)/(2)*Pi*(z)^(2))*sum(((- 1)^(n)* (Pi)^(2*n))/(1 * 3*(4*n + 1))*(z)^(4*n + 1), n = 0..infinity)+ sin((1)/(2)*Pi*(z)^(2))*sum(((- 1)^(n)* (Pi)^(2*n + 1))/(1 * 3*(4*n + 3))*(z)^(4*n + 3), n = 0..infinity) FresnelC[z] == Cos[Divide[1,2]*Pi*(z)^(2)]*Sum[Divide[(- 1)^(n)* (Pi)^(2*n),1 * 3*(4*n + 1)]*(z)^(4*n + 1), {n, 0, Infinity}, GenerateConditions->None]+ Sin[Divide[1,2]*Pi*(z)^(2)]*Sum[Divide[(- 1)^(n)* (Pi)^(2*n + 1),1 * 3*(4*n + 3)]*(z)^(4*n + 3), {n, 0, Infinity}, GenerateConditions->None] Failure Failure
Failed [7 / 7]
7/7]: [[.6549946728+.3747413995*I <- {z = 1/2*3^(1/2)+1/2*I}
-.3747413995+.6549946728*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [7 / 7]
{Complex[0.6549946726974499, 0.37474139987534255] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.37474139987534216, 0.6549946726974494] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.6.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}(\frac{1}{2}\pi)^{2n+1}}{(2n+1)!(4n+3)}z^{4n+3}} FresnelS(z) = sum(((- 1)^(n)*((1)/(2)*Pi)^(2*n + 1))/(factorial(2*n + 1)*(4*n + 3))*(z)^(4*n + 3), n = 0..infinity) FresnelS[z] == Sum[Divide[(- 1)^(n)*(Divide[1,2]*Pi)^(2*n + 1),(2*n + 1)!*(4*n + 3)]*(z)^(4*n + 3), {n, 0, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 7]
7.6.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = -\cos@{\tfrac{1}{2}\pi z^{2}}\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n+1}}{1\cdot 3\cdots(4n+3)}z^{4n+3}+\sin@{\tfrac{1}{2}\pi z^{2}}\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n}}{1\cdot 3\cdots(4n+1)}z^{4n+1}} FresnelS(z) = - cos((1)/(2)*Pi*(z)^(2))*sum(((- 1)^(n)* (Pi)^(2*n + 1))/(1 * 3*(4*n + 3))*(z)^(4*n + 3), n = 0..infinity)+ sin((1)/(2)*Pi*(z)^(2))*sum(((- 1)^(n)* (Pi)^(2*n))/(1 * 3*(4*n + 1))*(z)^(4*n + 1), n = 0..infinity) FresnelS[z] == - Cos[Divide[1,2]*Pi*(z)^(2)]*Sum[Divide[(- 1)^(n)* (Pi)^(2*n + 1),1 * 3*(4*n + 3)]*(z)^(4*n + 3), {n, 0, Infinity}, GenerateConditions->None]+ Sin[Divide[1,2]*Pi*(z)^(2)]*Sum[Divide[(- 1)^(n)* (Pi)^(2*n),1 * 3*(4*n + 1)]*(z)^(4*n + 1), {n, 0, Infinity}, GenerateConditions->None] Failure Failure
Failed [7 / 7]
7/7]: [[.306970168e-1+.2085514294*I <- {z = 1/2*3^(1/2)+1/2*I}
.2085514294-.306970168e-1*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [7 / 7]
{Complex[0.030697016764588636, 0.2085514288007122] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.2085514288007118, -0.030697016764589136] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.6.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{2z}{\sqrt{\pi}}\sum_{n=0}^{\infty}(-1)^{n}\left(\modsphBesseli{1}{2n}@{z^{2}}-\modsphBesseli{1}{2n+1}@{z^{2}}\right)} Error Erf[z] == Divide[2*z,Sqrt[Pi]]*Sum[(- 1)^(n)*(Sqrt[Divide[Pi, (z)^(2)]/2] BesselI[(-1)^(1-1)*(2*n + 1/2), 2*n]- Sqrt[Divide[Pi, (z)^(2)]/2] BesselI[(-1)^(1-1)*(2*n + 1 + 1/2), 2*n + 1]), {n, 0, Infinity}, GenerateConditions->None] Missing Macro Error Failure -
Failed [7 / 7]
{Plus[Complex[0.90211411820456, 0.25316491871645536], Times[Complex[-0.9772050238058398, -0.5641895835477562], NSum[Times[Power[-1, n], Plus[Times[Power[Power[E, Times[Complex[0, Rational[-1, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[2, n]], Times[2, n]]], Times[-1, Power[Power[E, Times[Complex[0, Rational[-1, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[3, 2], Times[2, n]], Plus[1, Times[2, n]]]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[-0.9777263798592635, 0.8570608779788039], Times[Complex[0.5641895835477561, -0.9772050238058398], NSum[Times[Power[-1, n], Plus[Times[Power[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[2, n]], Times[2, n]
7.6.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@{az} = \frac{2z}{\sqrt{\pi}}e^{(\frac{1}{2}-a^{2})z^{2}}\sum_{n=0}^{\infty}\ChebyshevpolyT{2n+1}@{a}\modsphBesseli{1}{n}@{\tfrac{1}{2}z^{2}}} Error Erf[a*z] == Divide[2*z,Sqrt[Pi]]*Exp[(Divide[1,2]- (a)^(2))* (z)^(2)]*Sum[ChebyshevT[2*n + 1, a]*Sqrt[Divide[Pi, Divide[1,2]*(z)^(2)]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], {n, 0, Infinity}, GenerateConditions->None] Missing Macro Error Aborted - Skipped - Because timed out
7.6.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = z\sum_{n=0}^{\infty}\sphBesselJ{2n}@{\tfrac{1}{2}\pi z^{2}}} Error FresnelC[z] == z*Sum[SphericalBesselJ[2*n, Divide[1,2]*Pi*(z)^(2)], {n, 0, Infinity}, GenerateConditions->None] Missing Macro Error Failure - Skipped - Because timed out
7.6.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = z\sum_{n=0}^{\infty}\sphBesselJ{2n+1}@{\tfrac{1}{2}\pi z^{2}}} Error FresnelS[z] == z*Sum[SphericalBesselJ[2*n + 1, Divide[1,2]*Pi*(z)^(2)], {n, 0, Infinity}, GenerateConditions->None] Missing Macro Error Failure - Skipped - Because timed out
7.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{2}{\pi}e^{-z^{2}}\int_{0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\diff{t}} erfc(z) = (2)/(Pi)*exp(- (z)^(2))*int((exp(- (z)^(2)* (t)^(2)))/((t)^(2)+ 1), t = 0..infinity) Erfc[z] == Divide[2,Pi]*Exp[- (z)^(2)]*Integrate[Divide[Exp[- (z)^(2)* (t)^(2)],(t)^(2)+ 1], {t, 0, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 4]
7.7.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi i}\int_{-\infty}^{\infty}\frac{e^{-t^{2}}\diff{t}}{t-z} = \frac{2z}{\pi i}\int_{0}^{\infty}\frac{e^{-t^{2}}\diff{t}}{t^{2}-z^{2}}} (1)/(Pi*I)*int((exp(- (t)^(2)))/(t - z), t = - infinity..infinity) = (2*z)/(Pi*I)*int((exp(- (t)^(2)))/((t)^(2)- (z)^(2)), t = 0..infinity) Divide[1,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],t - z], {t, - Infinity, Infinity}, GenerateConditions->None] == Divide[2*z,Pi*I]*Integrate[Divide[Exp[- (t)^(2)],(t)^(2)- (z)^(2)], {t, 0, Infinity}, GenerateConditions->None] Failure Failure
Failed [7 / 7]
7/7]: [[.2137917882+.3702982391*I <- {z = 1/2*3^(1/2)+1/2*I, z = I}
.572853371e-1-.2137917880*I <- {z = -1/2+1/2*I*3^(1/2), z = I}
 Successful [Tested: 1]
7.7.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at^{2}+2izt}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{a}}e^{-z^{2}/a}+\frac{i}{\sqrt{a}}\DawsonsintF@{\frac{z}{\sqrt{a}}}} int(exp(- a*(t)^(2)+ 2*I*z*t), t = 0..infinity) = (1)/(2)*sqrt((Pi)/(a))*exp(- (z)^(2)/ a)+(I)/(sqrt(a))*dawson((z)/(sqrt(a))) Integrate[Exp[- a*(t)^(2)+ 2*I*z*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[- (z)^(2)/ a]+Divide[I,Sqrt[a]]*DawsonF[Divide[z,Sqrt[a]]] Failure Successful Successful [Tested: 21] Successful [Tested: 21]
7.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{e^{-at}}{\sqrt{t+z^{2}}}\diff{t} = \sqrt{\frac{\pi}{a}}e^{az^{2}}\erfc@{\sqrt{a}z}} int((exp(- a*t))/(sqrt(t + (z)^(2))), t = 0..infinity) = sqrt((Pi)/(a))*exp(a*(z)^(2))*erfc(sqrt(a)*z) Integrate[Divide[Exp[- a*t],Sqrt[t + (z)^(2)]], {t, 0, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,a]]*Exp[a*(z)^(2)]*Erfc[Sqrt[a]*z] Successful Successful - Successful [Tested: 15]
7.7.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\frac{e^{-at^{2}}}{t^{2}+1}\diff{t} = \frac{\pi}{4}e^{a}\left(1-(\erf@@{\sqrt{a}})^{2}\right)} int((exp(- a*(t)^(2)))/((t)^(2)+ 1), t = 0..1) = (Pi)/(4)*exp(a)*(1 -(erf(sqrt(a)))^(2)) Integrate[Divide[Exp[- a*(t)^(2)],(t)^(2)+ 1], {t, 0, 1}, GenerateConditions->None] == Divide[Pi,4]*Exp[a]*(1 -(Erf[Sqrt[a]])^(2)) Failure Failure Successful [Tested: 3] Successful [Tested: 3]
7.7.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}e^{-(at^{2}+2bt+c)}\diff{t} = \frac{1}{2}\sqrt{\frac{\pi}{a}}e^{(b^{2}-ac)/a}\erfc@{\sqrt{a}x+\frac{b}{\sqrt{a}}}} int(exp(-(a*(t)^(2)+ 2*b*t + c)), t = x..infinity) = (1)/(2)*sqrt((Pi)/(a))*exp(((b)^(2)- a*c)/ a)*erfc(sqrt(a)*x +(b)/(sqrt(a))) Integrate[Exp[-(a*(t)^(2)+ 2*b*t + c)], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*Sqrt[Divide[Pi,a]]*Exp[((b)^(2)- a*c)/ a]*Erfc[Sqrt[a]*x +Divide[b,Sqrt[a]]] Failure Successful Successful [Tested: 300] Successful [Tested: 300]
7.7.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\diff{t} = \frac{\sqrt{\pi}}{4a}\left(e^{2ab}\erfc@{ax+(b/x)}+e^{-2ab}\erfc@{ax-(b/x)}\right)} int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = x..infinity) = (sqrt(Pi))/(4*a)*(exp(2*a*b)*erfc(a*x +(b/ x))+ exp(- 2*a*b)*erfc(a*x -(b/ x))) Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, x, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],4*a]*(Exp[2*a*b]*Erfc[a*x +(b/ x)]+ Exp[- 2*a*b]*Erfc[a*x -(b/ x)]) Failure Aborted Successful [Tested: 54] Skipped - Because timed out
7.7.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}\diff{t} = \frac{\sqrt{\pi}}{2a}e^{-2ab}} int(exp(- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))), t = 0..infinity) = (sqrt(Pi))/(2*a)*exp(- 2*a*b) Integrate[Exp[- (a)^(2)* (t)^(2)-((b)^(2)/ (t)^(2))], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],2*a]*Exp[- 2*a*b] Successful Successful - Successful [Tested: 9]
7.7.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\erf@@{t}\diff{t} = x\erf@@{x}+\frac{1}{\sqrt{\pi}}\left(e^{-x^{2}}-1\right)} int(erf(t), t = 0..x) = x*erf(x)+(1)/(sqrt(Pi))*(exp(- (x)^(2))- 1) Integrate[Erf[t], {t, 0, x}, GenerateConditions->None] == x*Erf[x]+Divide[1,Sqrt[Pi]]*(Exp[- (x)^(2)]- 1) Successful Successful - Successful [Tested: 3]
7.7.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{z} = \frac{1}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{e^{-\pi z^{2}t/2}}{\sqrt{t}(t^{2}+1)}\diff{t}} Fresnelf(z) = (1)/(Pi*sqrt(2))*int((exp(- Pi*(z)^(2)* t/ 2))/(sqrt(t)*((t)^(2)+ 1)), t = 0..infinity) FresnelF[z] == Divide[1,Pi*Sqrt[2]]*Integrate[Divide[Exp[- Pi*(z)^(2)* t/ 2],Sqrt[t]*((t)^(2)+ 1)], {t, 0, Infinity}, GenerateConditions->None] Failure Successful Successful [Tested: 4] Successful [Tested: 4]
7.7.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{z} = \frac{1}{\pi\sqrt{2}}\int_{0}^{\infty}\frac{\sqrt{t}e^{-\pi z^{2}t/2}}{t^{2}+1}\diff{t}} Fresnelg(z) = (1)/(Pi*sqrt(2))*int((sqrt(t)*exp(- Pi*(z)^(2)* t/ 2))/((t)^(2)+ 1), t = 0..infinity) FresnelG[z] == Divide[1,Pi*Sqrt[2]]*Integrate[Divide[Sqrt[t]*Exp[- Pi*(z)^(2)* t/ 2],(t)^(2)+ 1], {t, 0, Infinity}, GenerateConditions->None] Failure Successful Successful [Tested: 4] Successful [Tested: 4]
7.7.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{z}+i\auxFresnelf@{z} = e^{-\pi iz^{2}/2}\int_{z}^{\infty}e^{\pi it^{2}/2}\diff{t}} Fresnelg(z)+ I*Fresnelf(z) = exp(- Pi*I*(z)^(2)/ 2)*int(exp(Pi*I*(t)^(2)/ 2), t = z..infinity) FresnelG[z]+ I*FresnelF[z] == Exp[- Pi*I*(z)^(2)/ 2]*Integrate[Exp[Pi*I*(t)^(2)/ 2], {t, z, Infinity}, GenerateConditions->None] Successful Failure -
Failed [2 / 7]
{Complex[0.1740270274183789, -0.23657015577401255] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[-0.17402702741837872, 0.2365701557740125] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
7.7.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{z} = \frac{(2\pi)^{-3/2}}{2\pi i}\int_{c-i\infty}^{c+i\infty}\zeta^{-s}\EulerGamma@{s}\EulerGamma@{s+\tfrac{1}{2}}\*\EulerGamma@{s+\tfrac{3}{4}}\EulerGamma@{\tfrac{1}{4}-s}\diff{s}} Fresnelf(z) = ((2*Pi)^(- 3/ 2))/(2*Pi*I)*int((zeta)^(- s)* GAMMA(s)*GAMMA(s +(1)/(2))* GAMMA(s +(3)/(4))*GAMMA((1)/(4)- s), s = c - I*infinity..c + I*infinity) FresnelF[z] == Divide[(2*Pi)^(- 3/ 2),2*Pi*I]*Integrate[\[Zeta]^(- s)* Gamma[s]*Gamma[s +Divide[1,2]]* Gamma[s +Divide[3,4]]*Gamma[Divide[1,4]- s], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] Failure Aborted
Failed [300 / 300]
300/300]: [[.2811902531-.108667706*I <- {c = -1.5, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}
.2811902531-.108667706*I <- {c = -1.5, z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}
 Skipped - Because timed out
7.7.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{z} = \frac{(2\pi)^{-3/2}}{2\pi i}\int_{c-i\infty}^{c+i\infty}\zeta^{-s}\EulerGamma@{s}\EulerGamma@{s+\tfrac{1}{2}}\*\EulerGamma@{s+\tfrac{1}{4}}\EulerGamma@{\tfrac{3}{4}-s}\diff{s}} Fresnelg(z) = ((2*Pi)^(- 3/ 2))/(2*Pi*I)*int((zeta)^(- s)* GAMMA(s)*GAMMA(s +(1)/(2))* GAMMA(s +(1)/(4))*GAMMA((3)/(4)- s), s = c - I*infinity..c + I*infinity) FresnelG[z] == Divide[(2*Pi)^(- 3/ 2),2*Pi*I]*Integrate[\[Zeta]^(- s)* Gamma[s]*Gamma[s +Divide[1,2]]* Gamma[s +Divide[1,4]]*Gamma[Divide[3,4]- s], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None] Failure Aborted
Failed [300 / 300]
300/300]: [[.39257720e-1-.645221857e-1*I <- {c = -1.5, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}
.39257720e-1-.645221857e-1*I <- {c = -1.5, z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}
 Skipped - Because timed out
7.7.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\cos@{t^{2}}\diff{t} = \sqrt{\frac{\pi}{2}}\auxFresnelf@{\frac{a}{\sqrt{2\pi}}}} int(exp(- a*t)*cos((t)^(2)), t = 0..infinity) = sqrt((Pi)/(2))*Fresnelf((a)/(sqrt(2*Pi))) Integrate[Exp[- a*t]*Cos[(t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,2]]*FresnelF[Divide[a,Sqrt[2*Pi]]] Successful Aborted - Successful [Tested: 3]
7.7.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\sin@{t^{2}}\diff{t} = \sqrt{\frac{\pi}{2}}\auxFresnelg@{\frac{a}{\sqrt{2\pi}}}} int(exp(- a*t)*sin((t)^(2)), t = 0..infinity) = sqrt((Pi)/(2))*Fresnelg((a)/(sqrt(2*Pi))) Integrate[Exp[- a*t]*Sin[(t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,2]]*FresnelG[Divide[a,Sqrt[2*Pi]]] Successful Aborted - Successful [Tested: 3]
7.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \MillsM@{x} = \frac{\int_{x}^{\infty}e^{-t^{2}}\diff{t}}{e^{-x^{2}}}} Error Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] == Divide[Integrate[Exp[- (t)^(2)], {t, x, Infinity}, GenerateConditions->None],Exp[- (x)^(2)]] Missing Macro Error Failure -
Failed [3 / 3]
{Plus[-0.2849976548947546, Times[9.487735836358526, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]]], {Rule[x, 1.5]}
Plus[-0.545641360765047, Times[1.2840254166877414, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]]], {Rule[x, 0.5]}
7.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\int_{x}^{\infty}e^{-t^{2}}\diff{t}}{e^{-x^{2}}} = e^{x^{2}}\int_{x}^{\infty}e^{-t^{2}}\diff{t}} (int(exp(- (t)^(2)), t = x..infinity))/(exp(- (x)^(2))) = exp((x)^(2))*int(exp(- (t)^(2)), t = x..infinity) Divide[Integrate[Exp[- (t)^(2)], {t, x, Infinity}, GenerateConditions->None],Exp[- (x)^(2)]] == Exp[(x)^(2)]*Integrate[Exp[- (t)^(2)], {t, x, Infinity}, GenerateConditions->None] Successful Successful - Successful [Tested: 3]
7.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{x+\sqrt{x^{2}+2}} < \MillsM@{x}} Error Divide[1,x +Sqrt[(x)^(2)+ 2]] < Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] Missing Macro Error Failure -
Failed [3 / 3]
{Less[0.28077640640441515, Times[9.487735836358526, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]]], {Rule[x, 1.5]}
Less[0.5, Times[1.2840254166877414, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]]], {Rule[x, 0.5]}
7.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \MillsM@{x} \leq \frac{1}{x+\sqrt{x^{2}+(4/\pi)}}} Error Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] <= Divide[1,x +Sqrt[(x)^(2)+(4/ Pi)]] Missing Macro Error Failure -
Failed [3 / 3]
{LessEqual[Times[9.487735836358526, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]], 0.2961182351849971], {Rule[x, 1.5]}
LessEqual[Times[1.2840254166877414, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]], 0.5766361194388748], {Rule[x, 0.5]}
7.8.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sqrt{\pi}}{2\sqrt{\pi}x+2} \leq \MillsM@{x}} Error Divide[Sqrt[Pi],2*Sqrt[Pi]*x + 2] <= Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] Missing Macro Error Failure -
Failed [3 / 3]
{LessEqual[0.24222581297045487, Times[9.487735836358526, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]]], {Rule[x, 1.5]}
LessEqual[0.46984109573138116, Times[1.2840254166877414, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]]], {Rule[x, 0.5]}
7.8.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \MillsM@{x} < \frac{1}{x+1}} Error Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] < Divide[1,x + 1] Missing Macro Error Failure -
Failed [3 / 3]
{Less[Times[9.487735836358526, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]], 0.4], {Rule[x, 1.5]}
Less[Times[1.2840254166877414, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]], 0.6666666666666666], {Rule[x, 0.5]}
7.8.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \MillsM@{x} < \frac{2}{3x+\sqrt{x^{2}+4}}} Error Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] < Divide[2,3*x +Sqrt[(x)^(2)+ 4]] Missing Macro Error Failure -
Failed [3 / 3]
{Less[Times[9.487735836358526, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]], 0.2857142857142857], {Rule[x, 1.5]}
Less[Times[1.2840254166877414, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]], 0.5615528128088303], {Rule[x, 0.5]}
7.8.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x^{2}}{2x^{2}+1} \leq \frac{x^{2}(2x^{2}+5)}{4x^{4}+12x^{2}+3}} ((x)^(2))/(2*(x)^(2)+ 1) <= ((x)^(2)*(2*(x)^(2)+ 5))/(4*(x)^(4)+ 12*(x)^(2)+ 3) Divide[(x)^(2),2*(x)^(2)+ 1] <= Divide[(x)^(2)*(2*(x)^(2)+ 5),4*(x)^(4)+ 12*(x)^(2)+ 3] Failure Failure Successful [Tested: 3] Successful [Tested: 3]
7.8.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x^{2}(2x^{2}+5)}{4x^{4}+12x^{2}+3} \leq x\MillsM@{x}} Error Divide[(x)^(2)*(2*(x)^(2)+ 5),4*(x)^(4)+ 12*(x)^(2)+ 3] <= x*Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] Missing Macro Error Failure Skip - symbolical successful subtest
Failed [3 / 3]
{LessEqual[0.4253731343283582, Times[14.23160375453779, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]]], {Rule[x, 1.5]}
LessEqual[0.22, Times[0.6420127083438707, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]]], {Rule[x, 0.5]}
7.8.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x\MillsM@{x} < \frac{2x^{4}+9x^{2}+4}{4x^{4}+20x^{2}+15}} Error x*Exp[Power[x,2]] Int[Exp[-t^2], {t, x, Infinity}] < Divide[2*(x)^(4)+ 9*(x)^(2)+ 4,4*(x)^(4)+ 20*(x)^(2)+ 15] Missing Macro Error Failure Skip - symbolical successful subtest
Failed [3 / 3]
{Less[Times[14.23160375453779, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 1.5, DirectedInfinity[1]}]], 0.42834890965732086], {Rule[x, 1.5]}
Less[Times[0.6420127083438707, Int[Power[2.718281828459045, Times[-1.0, Power[t, 2]]] <- {t, 0.5, DirectedInfinity[1]}]], 0.31481481481481477], {Rule[x, 0.5]}
7.8.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2x^{4}+9x^{2}+4}{4x^{4}+20x^{2}+15} < \frac{x^{2}+1}{2x^{2}+3}} (2*(x)^(4)+ 9*(x)^(2)+ 4)/(4*(x)^(4)+ 20*(x)^(2)+ 15) < ((x)^(2)+ 1)/(2*(x)^(2)+ 3) Divide[2*(x)^(4)+ 9*(x)^(2)+ 4,4*(x)^(4)+ 20*(x)^(2)+ 15] < Divide[(x)^(2)+ 1,2*(x)^(2)+ 3] Failure Failure Successful [Tested: 3] Successful [Tested: 3]
7.8.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{at^{2}}\diff{t} < \frac{1}{3ax}\left(2e^{ax^{2}}+ax^{2}-2\right)} int(exp(a*(t)^(2)), t = 0..x) < (1)/(3*a*x)*(2*exp(a*(x)^(2))+ a*(x)^(2)- 2) Integrate[Exp[a*(t)^(2)], {t, 0, x}, GenerateConditions->None] < Divide[1,3*a*x]*(2*Exp[a*(x)^(2)]+ a*(x)^(2)- 2) Error Failure - Successful [Tested: 9]
7.8.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{t^{2}}\diff{t} < \frac{e^{x^{2}}-1}{x}} int(exp((t)^(2)), t = 0..x) < (exp((x)^(2))- 1)/(x) Integrate[Exp[(t)^(2)], {t, 0, x}, GenerateConditions->None] < Divide[Exp[(x)^(2)]- 1,x] Failure Failure Successful [Tested: 3] Successful [Tested: 3]
7.8.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{x} < \sqrt{1-\expe^{-4x^{2}/\cpi}}} erf(x) < sqrt(1 - exp(- 4*(x)^(2)/ Pi)) Erf[x] < Sqrt[1 - Exp[- 4*(x)^(2)/ Pi]] Failure Failure Successful [Tested: 3] Successful [Tested: 3]
7.10.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n+1]{\erf@@{z}}{z} = (-1)^{n}\frac{2}{\sqrt{\pi}}\HermitepolyH{n}@{z}e^{-z^{2}}} diff(erf(z), [z$(n + 1)]) = (- 1)^(n)*(2)/(sqrt(Pi))*HermiteH(n, z)*exp(- (z)^(2)) D[Erf[z], {z, n + 1}] == (- 1)^(n)*Divide[2,Sqrt[Pi]]*HermiteH[n, z]*Exp[- (z)^(2)] Failure Failure Manual Skip!
Failed [7 / 7]
{Plus[Complex[-3.565180358777125, 6.304771054937664], D[Complex[0.90211411820456, 0.25316491871645536] <- {Complex[0.8660254037844387, 0.49999999999999994], 4.0}]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[31.601340663516154, 7.3148164199817], D[Complex[-0.9777263798592635, 0.8570608779788039] <- {Complex[-0.4999999999999998, 0.8660254037844387], 4.0}]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.10#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\auxFresnelf@{z}}{z} = -\pi z\auxFresnelg@{z}} diff(Fresnelf(z), z) = - Pi*z*Fresnelg(z) D[FresnelF[z], z] == - Pi*z*FresnelG[z] Successful Successful - Successful [Tested: 7]
7.10#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{\auxFresnelg@{z}}{z} = \pi z\auxFresnelf@{z}-1} diff(Fresnelg(z), z) = Pi*z*Fresnelf(z)- 1 D[FresnelG[z], z] == Pi*z*FresnelF[z]- 1 Successful Successful - Successful [Tested: 7]
7.11.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}} erf(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2)) Erf[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], 0, (z)^(2)] Failure Failure
Failed [7 / 7]
7/7]: [[.756123263e-1-.1955582163*I <- {z = 1/2*3^(1/2)+1/2*I}
-1.938247417+2.376161732*I <- {z = -1/2+1/2*I*3^(1/2)}
Failed [2 / 7]
{Complex[-1.955452759718527, 1.7141217559576072] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[-1.8042282364091204, -0.5063298374329108] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}} erfc(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2), (z)^(2)) Erfc[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], (z)^(2)] Failure Failure
Failed [2 / 7]
2/7]: [[1.955452760-1.714121756*I <- {z = -1/2+1/2*I*3^(1/2)}
1.804228236+.5063298372*I <- {z = -1/2*3^(1/2)-1/2*I}
Failed [2 / 7]
{Complex[1.9554527597185267, -1.7141217559576072] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[1.8042282364091202, 0.5063298374329108] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}} erfc(z) = (z)/(sqrt(Pi))*Ei((1)/(2), (z)^(2)) Erfc[z] == Divide[z,Sqrt[Pi]]*ExpIntegralE[Divide[1,2], (z)^(2)] Failure Failure
Failed [2 / 7]
2/7]: [[2.000000000+.1e-9*I <- {z = -1/2+1/2*I*3^(1/2)}
2.000000000+.1e-9*I <- {z = -1/2*3^(1/2)-1/2*I}
Failed [2 / 7]
{Complex[2.0000000000000004, -7.771561172376096*^-16] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[1.9999999999999998, -5.551115123125783*^-17] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}} erf(z) = (2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2)) Erf[z] == Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] Successful Successful - Successful [Tested: 7]
7.11.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}} (2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2)) = (2*z)/(sqrt(Pi))*exp(- (z)^(2))*KummerM(1, (3)/(2), (z)^(2)) Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] == Divide[2*z,Sqrt[Pi]]*Exp[- (z)^(2)]*Hypergeometric1F1[1, Divide[3,2], (z)^(2)] Successful Successful - Successful [Tested: 7]
7.11.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}} erfc(z) = (1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2)) Erfc[z] == Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)] Failure Failure
Failed [2 / 7]
2/7]: [[1.955452760-1.714121756*I <- {z = -1/2+1/2*I*3^(1/2)}
1.804228236+.5063298372*I <- {z = -1/2*3^(1/2)-1/2*I}
Failed [2 / 7]
{Complex[1.9554527597185267, -1.7141217559576072] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[1.8042282364091202, 0.5063298374329108] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}} (1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2)) = (z)/(sqrt(Pi))*exp(- (z)^(2))*KummerU(1, (3)/(2), (z)^(2)) Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)] == Divide[z,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[1, Divide[3,2], (z)^(2)] Failure Failure
Failed [2 / 7]
2/7]: [[.4454723945e-1+1.714121756*I <- {z = -1/2+1/2*I*3^(1/2)}
.1957717634-.5063298372*I <- {z = -1/2*3^(1/2)-1/2*I}
Failed [2 / 7]
{Complex[0.04454724028147337, 1.7141217559576065] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[0.19577176359087947, -0.5063298374329108] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}} FresnelC(z)+ I*FresnelS(z) = z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2)) FresnelC[z]+ I*FresnelS[z] == z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)] Failure Successful Successful [Tested: 7] Successful [Tested: 7]
7.11.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}} z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2)) = z*exp(Pi*I*(z)^(2)/ 2)*KummerM(1, (3)/(2), -(1)/(2)*Pi*I*(z)^(2)) z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)] == z*Exp[Pi*I*(z)^(2)/ 2]*Hypergeometric1F1[1, Divide[3,2], -Divide[1,2]*Pi*I*(z)^(2)] Successful Successful Skip - symbolical successful subtest Successful [Tested: 7]
7.11.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}} FresnelC(z) = z*hypergeom([(1)/(4)], [(5)/(4),(1)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4)) FresnelC[z] == z*HypergeometricPFQ[{Divide[1,4]}, {Divide[5,4],Divide[1,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)] Successful Successful - Successful [Tested: 7]
7.11.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}} FresnelS(z) = (1)/(6)*Pi*(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4)) FresnelS[z] == Divide[1,6]*Pi*(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)] Successful Successful - Successful [Tested: 7]
7.13#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = 2\sqrt{n}} lambda = 2*sqrt(n) \[Lambda] == 2*Sqrt[n] Skipped - no semantic math Skipped - no semantic math - -
7.13#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = (2/\pi)\ln@{\pi\lambda}} alpha = (2/ Pi)* ln(Pi*lambda) \[Alpha] == (2/ Pi)* Log[Pi*\[Lambda]] Failure Failure
Failed [9 / 9]
9/9]: [[.421543168 <- {alpha = 1.5, n = 1}
.151839883 <- {alpha = 1.5, n = 2}
Failed [9 / 9]
{0.4215431680821278 <- {Rule[n, 1], Rule[α, 1.5]}
0.15183988257850767 <- {Rule[n, 2], Rule[α, 1.5]}
7.14.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{2iat}\erfc@{bt}\diff{t} = {\frac{1}{a\sqrt{\pi}}\DawsonsintF@{\frac{a}{b}}+\frac{i}{2a}\left(1-e^{-(a/b)^{2}}\right)}} int(exp(2*I*a*t)*erfc(b*t), t = 0..infinity) = (1)/(a*sqrt(Pi))*dawson((a)/(b))+(I)/(2*a)*(1 - exp(-(a/ b)^(2))) Integrate[Exp[2*I*a*t]*Erfc[b*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a*Sqrt[Pi]]*DawsonF[Divide[a,b]]+Divide[I,2*a]*(1 - Exp[-(a/ b)^(2)]) Failure Aborted Successful [Tested: 18] Successful [Tested: 3]
7.14.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\erf@{bt}\diff{t} = \frac{1}{a}e^{a^{2}/(4b^{2})}\erfc@{\frac{a}{2b}}} int(exp(- a*t)*erf(b*t), t = 0..infinity) = (1)/(a)*exp((a)^(2)/(4*(b)^(2)))*erfc((a)/(2*b)) Integrate[Exp[- a*t]*Erf[b*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a]*Exp[(a)^(2)/(4*(b)^(2))]*Erfc[Divide[a,2*b]] Successful Aborted - Skipped - Because timed out
7.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\erf@@{\sqrt{bt}}\diff{t} = \frac{1}{a}\sqrt{\frac{b}{a+b}}} int(exp(- a*t)*erf(sqrt(b*t)), t = 0..infinity) = (1)/(a)*sqrt((b)/(a + b)) Integrate[Exp[- a*t]*Erf[Sqrt[b*t]], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a]*Sqrt[Divide[b,a + b]] Failure Aborted Successful [Tested: 9] Skipped - Because timed out
7.14.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{(a-b)t}\erfc@{\sqrt{at}+\sqrt{\frac{c}{t}}}\diff{t} = \frac{e^{-2(\sqrt{ac}+\sqrt{bc})}}{\sqrt{b}(\sqrt{a}+\sqrt{b})}} int(exp((a - b)* t)*erfc(sqrt(a*t)+sqrt((c)/(t))), t = 0..infinity) = (exp(- 2*(sqrt(a*c)+sqrt(b*c))))/(sqrt(b)*(sqrt(a)+sqrt(b))) Integrate[Exp[(a - b)* t]*Erfc[Sqrt[a*t]+Sqrt[Divide[c,t]]], {t, 0, Infinity}, GenerateConditions->None] == Divide[Exp[- 2*(Sqrt[a*c]+Sqrt[b*c])],Sqrt[b]*(Sqrt[a]+Sqrt[b])] Failure Aborted Skipped - Because timed out Skipped - Because timed out
7.14.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\Fresnelcosint@{t}\diff{t} = \frac{1}{a}\auxFresnelf@{\frac{a}{\pi}}} int(exp(- a*t)*FresnelC(t), t = 0..infinity) = (1)/(a)*Fresnelf((a)/(Pi)) Integrate[Exp[- a*t]*FresnelC[t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a]*FresnelF[Divide[a,Pi]] Failure Successful Successful [Tested: 3] Successful [Tested: 3]
7.14.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\Fresnelsinint@{t}\diff{t} = \frac{1}{a}\auxFresnelg@{\frac{a}{\pi}}} int(exp(- a*t)*FresnelS(t), t = 0..infinity) = (1)/(a)*Fresnelg((a)/(Pi)) Integrate[Exp[- a*t]*FresnelS[t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,a]*FresnelG[Divide[a,Pi]] Failure Successful Successful [Tested: 3] Successful [Tested: 3]
7.14.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\Fresnelcosint@{\sqrt{\frac{2t}{\pi}}}\diff{t} = \frac{(\sqrt{a^{2}+1}+a)^{\frac{1}{2}}}{2a\sqrt{a^{2}+1}}} int(exp(- a*t)*FresnelC(sqrt((2*t)/(Pi))), t = 0..infinity) = ((sqrt((a)^(2)+ 1)+ a)^((1)/(2)))/(2*a*sqrt((a)^(2)+ 1)) Integrate[Exp[- a*t]*FresnelC[Sqrt[Divide[2*t,Pi]]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Sqrt[(a)^(2)+ 1]+ a)^(Divide[1,2]),2*a*Sqrt[(a)^(2)+ 1]] Successful Failure - Successful [Tested: 3]
7.14.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\Fresnelsinint@{\sqrt{\frac{2t}{\pi}}}\diff{t} = \frac{(\sqrt{a^{2}+1}-a)^{\frac{1}{2}}}{2a\sqrt{a^{2}+1}}} int(exp(- a*t)*FresnelS(sqrt((2*t)/(Pi))), t = 0..infinity) = ((sqrt((a)^(2)+ 1)- a)^((1)/(2)))/(2*a*sqrt((a)^(2)+ 1)) Integrate[Exp[- a*t]*FresnelS[Sqrt[Divide[2*t,Pi]]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Sqrt[(a)^(2)+ 1]- a)^(Divide[1,2]),2*a*Sqrt[(a)^(2)+ 1]] Failure Failure Successful [Tested: 3] Successful [Tested: 3]
7.17#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \inverf@@{x}} Error y == InverseErf[x] Missing Macro Error Failure -
Failed [6 / 18]
{-1.9769362762044698 <- {Rule[x, 0.5], Rule[y, -1.5]}
1.0230637237955302 <- {Rule[x, 0.5], Rule[y, 1.5]}
7.17#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \inverfc@@{x}} Error y == InverseErfc[x] Missing Macro Error Failure -
Failed [18 / 18]
{-1.02306372379553 <- {Rule[x, 1.5], Rule[y, -1.5]}
1.97693627620447 <- {Rule[x, 1.5], Rule[y, 1.5]}
7.18#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{-1}@{z} = \frac{2}{\sqrt{\pi}}e^{-z^{2}}} erfc(- 1, z) = (2)/(sqrt(Pi))*exp(- (z)^(2)) I^(- 1)*Erfc[z] == Divide[2,Sqrt[Pi]]*Exp[- (z)^(2)] Successful Failure -
Failed [7 / 7]
{Complex[-0.6965576261018753, 0.4234600295072003] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-2.0623272173358496, -3.394891496894652] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.18#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{0}@{z} = \erfc@@{z}} erfc(0, z) = erfc(z) I^(0)*Erfc[z] == Erfc[z] Successful Successful - Successful [Tested: 7]
7.18.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{n}@{z} = \int_{z}^{\infty}\repinterfc{n-1}@{t}\diff{t}} erfc(n, z) = int(erfc(n - 1, t), t = z..infinity) I^(n)*Erfc[z] == Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}, GenerateConditions->None] Failure Failure
Failed [12 / 21]
12/21]: [[Float(undefined)-.9036864554e-1*I <- {z = 1/2*3^(1/2)+1/2*I, n = 1}
Float(undefined)-.2674601677e-1*I <- {z = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [21 / 21]
{Complex[0.24282268468866475, 0.18825452738900728] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.18825452738900728, 0.24282268468866475] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{\infty}\repinterfc{n-1}@{t}\diff{t} = \frac{2}{\sqrt{\pi}}\int_{z}^{\infty}\frac{(t-z)^{n}}{n!}e^{-t^{2}}\diff{t}} int(erfc(n - 1, t), t = z..infinity) = (2)/(sqrt(Pi))*int(((t - z)^(n))/(factorial(n))*exp(- (t)^(2)), t = z..infinity) Integrate[I^(n - 1)*Erfc[t], {t, z, Infinity}, GenerateConditions->None] == Divide[2,Sqrt[Pi]]*Integrate[Divide[(t - z)^(n),(n)!]*Exp[- (t)^(2)], {t, z, Infinity}, GenerateConditions->None] Failure Failure
Failed [12 / 21]
12/21]: [[Float(undefined) <- {z = 1/2*3^(1/2)+1/2*I, n = 1}
Float(undefined) <- {z = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [13 / 21]
{Complex[0.09296765524307439, 0.0370882508190411] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.008358539694265255, 0.09727600825382138] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\repinterfc{n}@{z} = -\repinterfc{n-1}@{z}} diff(erfc(n, z), z) = - erfc(n - 1, z) D[I^(n)*Erfc[z], z] == - I^(n - 1)*Erfc[z] Successful Failure -
Failed [7 / 7]
{Complex[0.4234600295072003, 0.6965576261018753] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-3.394891496894652, 2.0623272173358496] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.18.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{z^{2}}\erfc@@{z}\right) = (-1)^{n}2^{n}n!e^{z^{2}}\repinterfc{n}@{z}} diff(exp((z)^(2))*erfc(z), [z$(n)]) = (- 1)^(n)* (2)^(n)* factorial(n)*exp((z)^(2))*erfc(n, z) D[Exp[(z)^(2)]*Erfc[z], {z, n}] == (- 1)^(n)* (2)^(n)* (n)!*Exp[(z)^(2)]*I^(n)*Erfc[z] Failure Failure Skipped - Because timed out
Failed [7 / 7]
{Complex[-7.3936292130611685, -19.806900214215183] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-48.524741574815884, -12.92653708276189] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.18.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{W}{z}+2z\deriv{W}{z}-2nW = 0} diff(W, [z$(2)])+ 2*z*diff(W, z)- 2*n*W = 0 D[W, {z, 2}]+ 2*z*D[W, z]- 2*n*W == 0 Failure Failure
Failed [210 / 210]
210/210]: [[-1.732050808-1.000000000*I <- {W = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}
-3.464101616-2.*I <- {W = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [210 / 210]
{Complex[-1.7320508075688774, -0.9999999999999999] <- {Rule[n, 1], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-3.464101615137755, -1.9999999999999998] <- {Rule[n, 2], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{n}@{z} = \sum_{k=0}^{\infty}\frac{(-1)^{k}z^{k}}{2^{n-k}k!\EulerGamma@{1+\frac{1}{2}(n-k)}}} erfc(n, z) = sum(((- 1)^(k)* (z)^(k))/((2)^(n - k)* factorial(k)*GAMMA(1 +(1)/(2)*(n - k))), k = 0..infinity) I^(n)*Erfc[z] == Sum[Divide[(- 1)^(k)* (z)^(k),(2)^(n - k)* (k)!*Gamma[1 +Divide[1,2]*(n - k)]], {k, 0, Infinity}, GenerateConditions->None] Failure Failure
Failed [21 / 21]
21/21]: [[-.8660254034-.4999999991*I <- {z = 1/2*3^(1/2)+1/2*I, n = 1}
.4999999999+.4330127014*I <- {z = 1/2*3^(1/2)+1/2*I, n = 2}
Failed [21 / 21]
{Complex[0.2428226846886648, 0.18825452738900733] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.09528687214593286, 0.27991093550770596] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{n}@{z} = -\frac{z}{n}\repinterfc{n-1}@{z}+\frac{1}{2n}\repinterfc{n-2}@{z}} erfc(n, z) = -(z)/(n)*erfc(n - 1, z)+(1)/(2*n)*erfc(n - 2, z) I^(n)*Erfc[z] == -Divide[z,n]*I^(n - 1)*Erfc[z]+Divide[1,2*n]*I^(n - 2)*Erfc[z] Successful Failure -
Failed [7 / 7]
{Complex[-0.36581044505750443, -0.05743209207542904] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.9176954586385406, -3.02111135172986] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.18.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\repinterfc{n}@{z}+\repinterfc{n}@{-z} = \frac{i^{-n}}{2^{n-1}n!}\HermitepolyH{n}@{iz}} (- 1)^(n)* erfc(n, z)+ erfc(n, - z) = ((I)^(- n))/((2)^(n - 1)* factorial(n))*HermiteH(n, I*z) (- 1)^(n)* I^(n)*Erfc[z]+ I^(n)*Erfc[- z] == Divide[(I)^(- n),(2)^(n - 1)* (n)!]*HermiteH[n, I*z] Failure Failure Successful [Tested: 21]
Failed [21 / 21]
{Complex[-2.2383806450017882, 0.8042282364091201] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-3.0, -0.8660254037844386] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{n}@{z} = e^{-z^{2}}\left(\frac{1}{2^{n}\EulerGamma@{\tfrac{1}{2}n+1}}\KummerconfhyperM@{\tfrac{1}{2}n+\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}-\frac{z}{2^{n-1}\EulerGamma@{\tfrac{1}{2}n+\tfrac{1}{2}}}\KummerconfhyperM@{\tfrac{1}{2}n+1}{\tfrac{3}{2}}{z^{2}}\right)} erfc(n, z) = exp(- (z)^(2))*((1)/((2)^(n)* GAMMA((1)/(2)*n + 1))*KummerM((1)/(2)*n +(1)/(2), (1)/(2), (z)^(2))-(z)/((2)^(n - 1)* GAMMA((1)/(2)*n +(1)/(2)))*KummerM((1)/(2)*n + 1, (3)/(2), (z)^(2))) I^(n)*Erfc[z] == Exp[- (z)^(2)]*(Divide[1,(2)^(n)* Gamma[Divide[1,2]*n + 1]]*Hypergeometric1F1[Divide[1,2]*n +Divide[1,2], Divide[1,2], (z)^(2)]-Divide[z,(2)^(n - 1)* Gamma[Divide[1,2]*n +Divide[1,2]]]*Hypergeometric1F1[Divide[1,2]*n + 1, Divide[3,2], (z)^(2)]) Failure Failure Successful [Tested: 21]
Failed [21 / 21]
{Complex[0.24282268468866477, 0.18825452738900755] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.09528687214593284, 0.27991093550770596] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{n}@{z} = \frac{e^{-z^{2}}}{2^{n}\sqrt{\pi}}\KummerconfhyperU@{\tfrac{1}{2}n+\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}} erfc(n, z) = (exp(- (z)^(2)))/((2)^(n)*sqrt(Pi))*KummerU((1)/(2)*n +(1)/(2), (1)/(2), (z)^(2)) I^(n)*Erfc[z] == Divide[Exp[- (z)^(2)],(2)^(n)*Sqrt[Pi]]*HypergeometricU[Divide[1,2]*n +Divide[1,2], Divide[1,2], (z)^(2)] Failure Failure
Failed [6 / 21]
6/21]: [[1.000000000-1.732050808*I <- {z = -1/2+1/2*I*3^(1/2), n = 1}
.1727305880-1.014340238*I <- {z = -1/2+1/2*I*3^(1/2), n = 2}
Failed [21 / 21]
{Complex[0.24282268468866502, 0.1882545273890069] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.09528687214593298, 0.2799109355077059] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.18.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \repinterfc{n}@{z} = \frac{e^{-z^{2}/2}}{\sqrt{2^{n-1}\pi}}\paraU@{n+\tfrac{1}{2}}{z\sqrt{2}}} erfc(n, z) = (exp(- (z)^(2)/ 2))/(sqrt((2)^(n - 1)* Pi))*CylinderU(n +(1)/(2), z*sqrt(2)) I^(n)*Erfc[z] == Divide[Exp[- (z)^(2)/ 2],Sqrt[(2)^(n - 1)* Pi]]*ParabolicCylinderD[- 1/2 -(n +Divide[1,2]), z*Sqrt[2]] Failure Failure Successful [Tested: 21]
Failed [21 / 21]
{Complex[0.24282268468866486, 0.1882545273890072] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.09528687214593298, 0.2799109355077059] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.20.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{x}e^{-(t-m)^{2}/(2\sigma^{2})}\diff{t} = \frac{1}{2}\erfc@{\frac{m-x}{\sigma\sqrt{2}}}} (1)/(sigma*sqrt(2*Pi))*int(exp(-(t - m)^(2)/(2*(sigma)^(2))), t = - infinity..x) = (1)/(2)*erfc((m - x)/(sigma*sqrt(2))) Divide[1,\[Sigma]*Sqrt[2*Pi]]*Integrate[Exp[-(t - m)^(2)/(2*\[Sigma]^(2))], {t, - Infinity, x}, GenerateConditions->None] == Divide[1,2]*Erfc[Divide[m - x,\[Sigma]*Sqrt[2]]] Failure Failure
Failed [54 / 90]
54/90]: [[Float(undefined)+Float(undefined)*I <- {sigma = -1/2+1/2*I*3^(1/2), x = 1.5, m = 1}
Float(undefined)+Float(undefined)*I <- {sigma = -1/2+1/2*I*3^(1/2), x = 1.5, m = 2}
Failed [45 / 90]
{Complex[-1.0, -1.942890293094024*^-16] <- {Rule[m, 1], Rule[x, 1.5], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[-1.0, -1.6653345369377348*^-16] <- {Rule[m, 2], Rule[x, 1.5], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
7.20.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\erfc@{\frac{m-x}{\sigma\sqrt{2}}} = Q\left(\frac{m-x}{\sigma}\right)} (1)/(2)*erfc((m - x)/(sigma*sqrt(2))) = Q*((m - x)/(sigma)) Divide[1,2]*Erfc[Divide[m - x,\[Sigma]*Sqrt[2]]] == Q*(Divide[m - x,\[Sigma]]) Failure Failure
Failed [300 / 300]
300/300]: [[1.172485186-.9158452425e-1*I <- {Q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, x = 1.5, m = 1}
-.1724851867+.9158452425e-1*I <- {Q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, x = 1.5, m = 2}
Failed [300 / 300]
{Complex[1.1724851867610806, -0.09158452430796671] <- {Rule[m, 1], Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.1724851867610806, 0.09158452430796671] <- {Rule[m, 2], Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
7.20.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q\left(\frac{m-x}{\sigma}\right) = P\left(\frac{x-m}{\sigma}\right)} Q*((m - x)/(sigma)) = P*((x - m)/(sigma)) Q*(Divide[m - x,\[Sigma]]) == P*(Divide[x - m,\[Sigma]]) Failure Failure
Failed [240 / 300]
240/300]: [[-1.0 <- {P = 1/2*3^(1/2)+1/2*I, Q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, x = 1.5, m = 1}
1.0 <- {P = 1/2*3^(1/2)+1/2*I, Q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, x = 1.5, m = 2}
Failed [240 / 300]
{Complex[-1.0, 0.0] <- {Rule[m, 1], Rule[P, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.0, 0.0] <- {Rule[m, 2], Rule[P, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
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