Struve and Related Functions - 11.10 Anger–Weber Functions

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
11.10.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}}
\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)

AngerJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]
Failure Aborted Successful [Tested: 70] Skipped - Because timed out
11.10.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}}
\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE(nu, z) = (1)/(Pi)*int(sin(nu*theta - z*sin(theta)), theta = 0..Pi)

WeberE[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]
Failure Failure Successful [Tested: 70] Skipped - Because timed out
11.10.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{2\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta} = (1+\cos@{2\pi\nu})\,\AngerJ{\nu}@{z}+\sin@{2\pi\nu}\WeberE{\nu}@{z}}
\frac{1}{\pi}\int_{0}^{2\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta} = (1+\cos@{2\pi\nu})\,\AngerJ{\nu}@{z}+\sin@{2\pi\nu}\WeberE{\nu}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..2*Pi) = (1 + cos(2*Pi*nu))*AngerJ(nu, z)+ sin(2*Pi*nu)*WeberE(nu, z)

Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == (1 + Cos[2*Pi*\[Nu]])*AngerJ[\[Nu], z]+ Sin[2*Pi*\[Nu]]*WeberE[\[Nu], z]
Failure Failure Successful [Tested: 70] Skipped - Because timed out
11.10.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)}
\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(nu, z) = cos((1)/(2)*Pi*nu)*S[1](nu , z)+ sin((1)/(2)*Pi*nu)*S[2](nu , z)

AngerJ[\[Nu], z] == Cos[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 1][\[Nu], z]+ Sin[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 2][\[Nu], z]
Failure Failure
Failed [300 / 300]
Result: .4325617835-.4216939044*I-(1.695493166+.2075033380*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = 1/2*3^(1/2)+1/2*I}


Result: .4325617835-.4216939044*I+(.1404557731-.4337646272*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 Error
11.10.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)}
\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE(nu, z) = sin((1)/(2)*Pi*nu)*S[1](nu , z)- cos((1)/(2)*Pi*nu)*S[2](nu , z)

WeberE[\[Nu], z] == Sin[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 1][\[Nu], z]- Cos[Divide[1,2]*Pi*\[Nu]]*Subscript[S, 2][\[Nu], z]
Failure Failure
Failed [300 / 300]
Result: .6530158617-.8867638354e-1*I-(.3667170623+1.402184312*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = 1/2*3^(1/2)+1/2*I}


Result: .6530158617-.8867638354e-1*I-(.4337646272+.1404557731*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I, S[2] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 Error
11.10.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{1}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu+1}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!1}}}
S_{1}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu+1}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!1}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(k+\tfrac{1}{2}\nu+1)} > 0, \realpart@@{(k-\tfrac{1}{2}\nu+1)} > 0} 
S[1](nu , z) = sum(((- 1)^(k)*((1)/(2)*z)^(2*k))/(GAMMA(k +(1)/(2)*nu + 1)*GAMMA(k -(1)/(2)*nu + 1)), k = 0..infinity)

Subscript[S, 1][\[Nu], z] == Sum[Divide[(- 1)^(k)*(Divide[1,2]*z)^(2*k),Gamma[k +Divide[1,2]*\[Nu]+ 1]*Gamma[k -Divide[1,2]*\[Nu]+ 1]], {k, 0, Infinity}, GenerateConditions->None]
Failure Failure
Failed [300 / 300]
Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.6234597010+.4805214665*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = 1/2*3^(1/2)+1/2*I}


Result: (-.5000000000+.8660254040*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.6234597010+.4805214665*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[1] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 Error
11.10.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{2}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k+1}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}}}
S_{2}(\nu,z) = \sum_{k=0}^{\infty}\frac{(-1)^{k}(\tfrac{1}{2}z)^{2k+1}}{\EulerGamma@{k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}\EulerGamma@{k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(k+\tfrac{1}{2}\nu+\tfrac{3}{2})} > 0, \realpart@@{(k-\tfrac{1}{2}\nu+\tfrac{3}{2})} > 0} 
S[2](nu , z) = sum(((- 1)^(k)*((1)/(2)*z)^(2*k + 1))/(GAMMA(k +(1)/(2)*nu +(3)/(2))*GAMMA(k -(1)/(2)*nu +(3)/(2))), k = 0..infinity)

Subscript[S, 2][\[Nu], z] == Sum[Divide[(- 1)^(k)*(Divide[1,2]*z)^(2*k + 1),Gamma[k +Divide[1,2]*\[Nu]+Divide[3,2]]*Gamma[k -Divide[1,2]*\[Nu]+Divide[3,2]]], {k, 0, Infinity}, GenerateConditions->None]
Failure Failure
Failed [300 / 300]
Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.4892722811e-1+.1117224133*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[2] = 1/2*3^(1/2)+1/2*I}


Result: (-.5000000000+.8660254040*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.4892722811e-1+.1117224133*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, S[2] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 Error
11.10#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}}
\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(nu, - z) = AngerJ(- nu, z)

AngerJ[\[Nu], - z] == AngerJ[- \[Nu], z]
Successful Successful - Successful [Tested: 70]
11.10#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}}
\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE(nu, - z) = - WeberE(- nu, z)

WeberE[\[Nu], - z] == - WeberE[- \[Nu], z]
Successful Successful - Successful [Tested: 70]
11.10.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}}
\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sin(Pi*nu)*AngerJ(nu, z) = cos(Pi*nu)*WeberE(nu, z)- WeberE(- nu, z)

Sin[Pi*\[Nu]]*AngerJ[\[Nu], z] == Cos[Pi*\[Nu]]*WeberE[\[Nu], z]- WeberE[- \[Nu], z]
Successful Failure - Successful [Tested: 70]
11.10.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}}
\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sin(Pi*nu)*WeberE(nu, z) = AngerJ(- nu, z)- cos(Pi*nu)*AngerJ(nu, z)

Sin[Pi*\[Nu]]*WeberE[\[Nu], z] == AngerJ[- \[Nu], z]- Cos[Pi*\[Nu]]*AngerJ[\[Nu], z]
Successful Failure - Successful [Tested: 70]
11.10.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})}
\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(nu, z) = (sin(Pi*nu))/(Pi)*(LommelS1(0, nu, z)- nu*LommelS1(- 1, nu, z))

Error
Successful Missing Macro Error - -
11.10.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu}@{z} = -\frac{1}{\pi}(1+\cos@{\pi\nu})\Lommels{0}{\nu}@{z}\\ -\frac{\nu}{\pi}(1-\cos@{\pi\nu})\Lommels{-1}{\nu}@{z}}
\WeberE{\nu}@{z} = -\frac{1}{\pi}(1+\cos@{\pi\nu})\Lommels{0}{\nu}@{z}\\ -\frac{\nu}{\pi}(1-\cos@{\pi\nu})\Lommels{-1}{\nu}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE(nu, z) = -(1)/(Pi)*(1 + cos(Pi*nu))*LommelS1(0, nu, z)*; -(nu)/(Pi)*(1 - cos(Pi*nu))* LommelS1(- 1, nu, z)

Error
Successful Missing Macro Error - -
11.10.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\}
\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(-(1)/(2), z) = WeberE((1)/(2), z)

AngerJ[-Divide[1,2], z] == WeberE[Divide[1,2], z]
Successful Successful - Successful [Tested: 7]
11.10.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})}
\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE((1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* cos(z)- A[-](chi)* sin(z))

WeberE[Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Cos[z]- Subscript[A, -][\[Chi]]* Sin[z])
Error Failure - Error
11.10.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\}
\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ((1)/(2), z) = - WeberE(-(1)/(2), z)

AngerJ[Divide[1,2], z] == - WeberE[-Divide[1,2], z]
Successful Successful - Successful [Tested: 7]
11.10.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})}
-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
- WeberE(-(1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* sin(z)+ A[-](chi)* cos(z))

- WeberE[-Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Sin[z]+ Subscript[A, -][\[Chi]]* Cos[z])
Error Failure - Error
11.10#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}}
A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
A[+](chi) = FresnelC(chi)+ FresnelS(chi)

Subscript[A, +][\[Chi]] == FresnelC[\[Chi]]+ FresnelS[\[Chi]]
Error Failure - Error
11.10#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}}
A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
A[-](chi) = FresnelC(chi)- FresnelS(chi)

Subscript[A, -][\[Chi]] == FresnelC[\[Chi]]- FresnelS[\[Chi]]
Error Failure - Error
11.10#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \chi = (2z/\pi)^{\frac{1}{2}}}
\chi = (2z/\pi)^{\frac{1}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
chi = (2*z/Pi)^((1)/(2))
 
\[Chi] == (2*z/Pi)^(Divide[1,2])
 Skipped - no semantic math Skipped - no semantic math - -
11.10.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{n}@{z} = -\StruveH{n}@{z}+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\EulerGamma@{k+\tfrac{1}{2}}}{\EulerGamma@{n\!+\!\tfrac{1}{2}\!-\!k}}(\tfrac{1}{2}z)^{n-2k-1}}
\WeberE{n}@{z} = -\StruveH{n}@{z}+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\EulerGamma@{k+\tfrac{1}{2}}}{\EulerGamma@{n\!+\!\tfrac{1}{2}\!-\!k}}(\tfrac{1}{2}z)^{n-2k-1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(k+\tfrac{1}{2})} > 0, \realpart@@{(n+\tfrac{1}{2}-k)} > 0, \realpart@@{(n+n+\tfrac{3}{2})} > 0} 
WeberE(n, z) = - StruveH(n, z)+(1)/(Pi)*sum((GAMMA(k +(1)/(2)))/(GAMMA(n +(1)/(2)- k))*((1)/(2)*z)^(n - 2*k - 1), k = 0..m[1])

WeberE[n, z] == - StruveH[n, z]+Divide[1,Pi]*Sum[Divide[Gamma[k +Divide[1,2]],Gamma[n +Divide[1,2]- k]]*(Divide[1,2]*z)^(n - 2*k - 1), {k, 0, Subscript[m, 1]}, GenerateConditions->None]
Failure Failure Manual Skip!
Failed [210 / 210]
Result: Plus[0.6366197723675814, Times[-0.3183098861837907, DifferenceRoot[Function[{, }
Test Values: {Equal[Plus[Times[-1, Plus[-1, Times[2, ]], Plus[1, Times[2, ]], []], Times[Plus[-1, Times[-1, Power[-1, Rational[1, 3]]], Times[4, Power[, 2]]], [Plus[1, ]]], Times[Power[-1, Rational[1, 3]], [Plus[2, ]]]], 0], Equal[[0], 0], Equal[[1], 2]}]][Complex[1.8660254037844388, 0.49999999999999994]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Plus[Complex[0.18377629847393068, 0.10610329539459687], Times[Complex[-0.13783222385544802, -0.07957747154594766], DifferenceRoot[Function[{, }
Test Values: {Equal[Plus[Times[-1, Plus[-3, Times[2, ]], Plus[1, Times[2, ]], []], Times[Plus[-3, Times[-1, Power[-1, Rational[1, 3]]], Times[-4, ], Times[4, Power[, 2]]], [Plus[1, ]]], Times[Power[-1, Rational[1, 3]], [Plus[2, ]]]], 0], Equal[[0], 0], Equal[[1], Rational[4, 3]]}]][Complex[1.8660254037844388, 0.49999999999999994]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
11.10.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{-n}@{z} = -\StruveH{-n}@{z}+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\EulerGamma@{n\!-\!k\!-\!\tfrac{1}{2}}}{\EulerGamma@{k+\tfrac{3}{2}}}(\tfrac{1}{2}z)^{-n+2k+1}}
\WeberE{-n}@{z} = -\StruveH{-n}@{z}+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\EulerGamma@{n\!-\!k\!-\!\tfrac{1}{2}}}{\EulerGamma@{k+\tfrac{3}{2}}}(\tfrac{1}{2}z)^{-n+2k+1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(n-k-\tfrac{1}{2})} > 0, \realpart@@{(k+\tfrac{3}{2})} > 0, \realpart@@{(n+(-n)+\tfrac{3}{2})} > 0} 
WeberE(- n, z) = - StruveH(- n, z)+((- 1)^(n + 1))/(Pi)*sum((GAMMA(n - k -(1)/(2)))/(GAMMA(k +(3)/(2)))*((1)/(2)*z)^(- n + 2*k + 1), k = 0..m[2])

WeberE[- n, z] == - StruveH[- n, z]+Divide[(- 1)^(n + 1),Pi]*Sum[Divide[Gamma[n - k -Divide[1,2]],Gamma[k +Divide[3,2]]]*(Divide[1,2]*z)^(- n + 2*k + 1), {k, 0, Subscript[m, 2]}, GenerateConditions->None]
Failure Failure
Failed [210 / 210]
Result: -.5182370935+.1715162156*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m[2] = 1/2*3^(1/2)+1/2*I, n = 1}


Result: .1977910573+.6179671328e-1*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m[2] = 1/2*3^(1/2)+1/2*I, n = 2}

... skip entries to safe data
Failed [210 / 210]
Result: Complex[-0.5182370936641069, 0.17151621559870867]
Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.19779105745155356, 0.06179671324201291]
Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
11.10#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}}
m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
m[1] = floor((1)/(2)*n -(1)/(2))

Subscript[m, 1] == Floor[Divide[1,2]*n -Divide[1,2]]
Failure Failure
Failed [30 / 30]
Result: .8660254040+.5000000000*I
Test Values: {m[1] = 1/2*3^(1/2)+1/2*I, n = 1}


Result: .8660254040+.5000000000*I
Test Values: {m[1] = 1/2*3^(1/2)+1/2*I, n = 2}

... skip entries to safe data
Failed [30 / 30]
Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[n, 1], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[n, 2], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
11.10#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}}
m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
m[2] = ceil((1)/(2)*n -(3)/(2))

Subscript[m, 2] == Ceiling[Divide[1,2]*n -Divide[3,2]]
Failure Failure
Failed [30 / 30]
Result: 1.866025404+.5000000000*I
Test Values: {m[2] = 1/2*3^(1/2)+1/2*I, n = 1}


Result: .8660254040+.5000000000*I
Test Values: {m[2] = 1/2*3^(1/2)+1/2*I, n = 2}

... skip entries to safe data
Failed [30 / 30]
Result: Complex[1.8660254037844388, 0.49999999999999994]
Test Values: {Rule[n, 1], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[n, 2], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
11.10.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}}
\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(nu, 0) = (sin(Pi*nu))/(Pi*nu)
 
AngerJ[\[Nu], 0] == Divide[Sin[Pi*\[Nu]],Pi*\[Nu]]
 Skipped - no semantic math Skipped - no semantic math - -
11.10.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}}
\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE(nu, 0) = (1 - cos(Pi*nu))/(Pi*nu)
 
WeberE[\[Nu], 0] == Divide[1 - Cos[Pi*\[Nu]],Pi*\[Nu]]
 Skipped - no semantic math Skipped - no semantic math - -
11.10.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}}
\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(n+0+\tfrac{3}{2})} > 0} 
WeberE(0, z) = - StruveH(0, z)
 
WeberE[0, z] == - StruveH[0, z]
 Skipped - no semantic math Skipped - no semantic math - -
11.10.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}}
\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(n+1+\tfrac{3}{2})} > 0} 
WeberE(1, z) = (2)/(Pi)- StruveH(1, z)
 
WeberE[1, z] == Divide[2,Pi]- StruveH[1, z]
 Skipped - no semantic math Skipped - no semantic math - -
11.10.E29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{n}@{z} = \BesselJ{n}@{z}}
\AngerJ{n}@{z} = \BesselJ{n}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(n+k+1)} > 0} 
AngerJ(n, z) = BesselJ(n, z)

AngerJ[n, z] == BesselJ[n, z]
Failure Successful Successful [Tested: 7] Successful [Tested: 7]
11.10.E32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}}
\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
AngerJ(nu - 1, z)+ AngerJ(nu + 1, z) = (2*nu)/(z)*AngerJ(nu, z)-(2)/(Pi*z)*sin(Pi*nu)
 
AngerJ[\[Nu]- 1, z]+ AngerJ[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*AngerJ[\[Nu], z]-Divide[2,Pi*z]*Sin[Pi*\[Nu]]
 Failure Failure
Failed [3 / 70]
Result: .1812319651
Test Values: {nu = -3/2, z = 3/2}

Result: .1208213102
Test Values: {nu = -1/2, z = 3/2}

... skip entries to safe data
 Successful [Tested: 70]
11.10.E33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})}
\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
WeberE(nu - 1, z)+ WeberE(nu + 1, z) = (2*nu)/(z)*WeberE(nu, z)-(2)/(Pi*z)*(1 - cos(Pi*nu))
 
WeberE[\[Nu]- 1, z]+ WeberE[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*WeberE[\[Nu], z]-Divide[2,Pi*z]*(1 - Cos[Pi*\[Nu]])
 Failure Failure
Failed [3 / 70]
Result: .1812319648
Test Values: {nu = 3/2, z = 3/2}

Result: .1812319652
Test Values: {nu = -1/2, z = 3/2}

... skip entries to safe data
 Successful [Tested: 70]
11.10.E34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}}
2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
2*diff( AngerJ(nu, z), z$(1) ) = AngerJ(nu - 1, z)- AngerJ(nu + 1, z)
 
2*D[AngerJ[\[Nu], z], {z, 1}] == AngerJ[\[Nu]- 1, z]- AngerJ[\[Nu]+ 1, z]
 Failure Successful
Failed [3 / 70]
Result: -.1812319651
Test Values: {nu = -3/2, z = 3/2}

Result: -.1208213102
Test Values: {nu = -1/2, z = 3/2}

... skip entries to safe data
 Successful [Tested: 70]
11.10.E35 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}}
2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
2*diff( WeberE(nu, z), z$(1) ) = WeberE(nu - 1, z)- WeberE(nu + 1, z)
 
2*D[WeberE[\[Nu], z], {z, 1}] == WeberE[\[Nu]- 1, z]- WeberE[\[Nu]+ 1, z]
 Failure Successful
Failed [3 / 70]
Result: -.1812319648
Test Values: {nu = 3/2, z = 3/2}

Result: -.1812319652
Test Values: {nu = -1/2, z = 3/2}

... skip entries to safe data
 Successful [Tested: 70]
11.10.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}}
z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z*diff( AngerJ(nu, z), z$(1) )+ nu*AngerJ(nu, z) = + z*AngerJ(nu - 1, z)+(sin(Pi*nu))/(Pi)
 
z*D[AngerJ[\[Nu], z], {z, 1}]+ \[Nu]*AngerJ[\[Nu], z] == + z*AngerJ[\[Nu]- 1, z]+Divide[Sin[Pi*\[Nu]],Pi]
 Failure Failure
Failed [3 / 70]
Result: -.2718479477
Test Values: {nu = -3/2, z = 3/2}

Result: -.1812319655
Test Values: {nu = -1/2, z = 3/2}

... skip entries to safe data
 Successful [Tested: 70]
11.10.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}}
z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z*diff( AngerJ(nu, z), z$(1) )- nu*AngerJ(nu, z) = - z*AngerJ(nu + 1, z)-(sin(Pi*nu))/(Pi)
 
z*D[AngerJ[\[Nu], z], {z, 1}]- \[Nu]*AngerJ[\[Nu], z] == - z*AngerJ[\[Nu]+ 1, z]-Divide[Sin[Pi*\[Nu]],Pi]
 Successful Failure Skip - symbolical successful subtest Successful [Tested: 70]
11.10.E37 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}}
z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z*diff( WeberE(nu, z), z$(1) )+ nu*WeberE(nu, z) = + z*WeberE(nu - 1, z)+(1 - cos(Pi*nu))/(Pi)
 
z*D[WeberE[\[Nu], z], {z, 1}]+ \[Nu]*WeberE[\[Nu], z] == + z*WeberE[\[Nu]- 1, z]+Divide[1 - Cos[Pi*\[Nu]],Pi]
 Failure Failure
Failed [3 / 70]
Result: -.2718479477
Test Values: {nu = 3/2, z = 3/2}

Result: -.2718479472
Test Values: {nu = -1/2, z = 3/2}

... skip entries to safe data
 Successful [Tested: 70]
11.10.E37 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}}
z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z*diff( WeberE(nu, z), z$(1) )- nu*WeberE(nu, z) = - z*WeberE(nu + 1, z)-(1 - cos(Pi*nu))/(Pi)
 
z*D[WeberE[\[Nu], z], {z, 1}]- \[Nu]*WeberE[\[Nu], z] == - z*WeberE[\[Nu]+ 1, z]-Divide[1 - Cos[Pi*\[Nu]],Pi]
 Successful Failure Skip - symbolical successful subtest Successful [Tested: 70]
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