11.10: Difference between revisions

Latest revision as of 11:29, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
11.10.E1	${\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=\frac{1}{\pi}\int_{% 0}^{\pi}\cos\left(\nu\theta-z\sin\theta\right)\mathrm{d}\theta}}$ `\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}`		AngerJ(nu, z) = (1)/(Pi)int(cos(nutheta - 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	${\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(z\right)=\frac{1}{\pi}\int_{% 0}^{\pi}\sin\left(\nu\theta-z\sin\theta\right)\mathrm{d}\theta}}$ `\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}`		WeberE(nu, z) = (1)/(Pi)int(sin(nutheta - 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	${\displaystyle{\displaystyle\frac{1}{\pi}\int_{0}^{2\pi}\cos\left(\nu\theta-z% \sin\theta\right)\mathrm{d}\theta=(1+\cos\left(2\pi\nu\right))\,\mathbf{J}_{% \nu}\left(z\right)+\sin\left(2\pi\nu\right)\mathbf{E}_{\nu}\left(z\right)}}$ `\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}`		(1)/(Pi)int(cos(nutheta - zsin(theta)), theta = 0..2Pi) = (1 + cos(2Pinu))AngerJ(nu, z)+ sin(2Pinu)WeberE(nu, z)	Divide[1,Pi]Integrate[Cos[\[Nu]\[Theta]- zSin[\[Theta]]], {\[Theta], 0, 2Pi}, GenerateConditions->None] == (1 + Cos[2Pi\[Nu]])AngerJ[\[Nu], z]+ Sin[2Pi\[Nu]]WeberE[\[Nu], z]	Failure	Failure	Successful [Tested: 70]	Skipped - Because timed out
11.10.E8	${\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=\cos\left(\tfrac{1}% {2}\pi\nu\right)\,S_{1}(\nu,z)+\sin\left(\tfrac{1}{2}\pi\nu\right)\,S_{2}(\nu,% z)}}$ `\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)`		AngerJ(nu, z) = cos((1)/(2)Pinu)S[1](nu , z)+ sin((1)/(2)Pinu)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-.4216939044I-(1.695493166+.2075033380I)(.8660254040+.5000000000I, .8660254040+.5000000000I) Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[1] = 1/23^(1/2)+1/2I, S[2] = 1/23^(1/2)+1/2I} Result: .4325617835-.4216939044I+(.1404557731-.4337646272I)(.8660254040+.5000000000I, .8660254040+.5000000000I) Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[1] = 1/23^(1/2)+1/2I, S[2] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Error
11.10.E9	${\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(z\right)=\sin\left(\tfrac{1}% {2}\pi\nu\right)\,S_{1}(\nu,z)-\cos\left(\tfrac{1}{2}\pi\nu\right)\,S_{2}(\nu,% z)}}$ `\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)`		WeberE(nu, z) = sin((1)/(2)Pinu)S[1](nu , z)- cos((1)/(2)Pinu)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-1I-(.3667170623+1.402184312I)(.8660254040+.5000000000I, .8660254040+.5000000000I) Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[1] = 1/23^(1/2)+1/2I, S[2] = 1/23^(1/2)+1/2I} Result: .6530158617-.8867638354e-1I-(.4337646272+.1404557731I)(.8660254040+.5000000000I, .8660254040+.5000000000I) Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[1] = 1/23^(1/2)+1/2I, S[2] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Error
11.10.E10	${\displaystyle{\displaystyle S_{1}(\nu,z)=\sum_{k=0}^{\infty}\frac{(-1)^{k}(% \tfrac{1}{2}z)^{2k}}{\Gamma\left(k\!+\!\tfrac{1}{2}\nu+1\right)\Gamma\left(k\!% -\!\tfrac{1}{2}\nu\!+\!1\right)}}}$ `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}}`	${\displaystyle{\displaystyle\Re(k+\tfrac{1}{2}\nu+1)>0,\Re(k-\tfrac{1}{2}\nu+1% )>0}}$	S[1](nu , z) = sum(((- 1)^(k)((1)/(2)z)^(2k))/(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)^(2k),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+.5000000000I)(.8660254040+.5000000000I, .8660254040+.5000000000I)-.6234597010+.4805214665I Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[1] = 1/23^(1/2)+1/2I} Result: (-.5000000000+.8660254040I)(.8660254040+.5000000000I, .8660254040+.5000000000I)-.6234597010+.4805214665I Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[1] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Error
11.10.E11	${\displaystyle{\displaystyle S_{2}(\nu,z)=\sum_{k=0}^{\infty}\frac{(-1)^{k}(% \tfrac{1}{2}z)^{2k+1}}{\Gamma\left(k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}% \right)\Gamma\left(k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}\right)}}}$ `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}}}`	${\displaystyle{\displaystyle\Re(k+\tfrac{1}{2}\nu+\tfrac{3}{2})>0,\Re(k-\tfrac% {1}{2}\nu+\tfrac{3}{2})>0}}$	S[2](nu , z) = sum(((- 1)^(k)((1)/(2)z)^(2k + 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)^(2k + 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+.5000000000I)(.8660254040+.5000000000I, .8660254040+.5000000000I)-.4892722811e-1+.1117224133I Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[2] = 1/23^(1/2)+1/2I} Result: (-.5000000000+.8660254040I)(.8660254040+.5000000000I, .8660254040+.5000000000I)-.4892722811e-1+.1117224133I Test Values: {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, S[2] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Error
11.10#Ex1	${\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(-z\right)=\mathbf{J}_{-\nu}% \left(z\right)}}$ `\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}`		AngerJ(nu, - z) = AngerJ(- nu, z)	AngerJ[\[Nu], - z] == AngerJ[- \[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
11.10#Ex2	${\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(-z\right)=-\mathbf{E}_{-\nu}% \left(z\right)}}$ `\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}`		WeberE(nu, - z) = - WeberE(- nu, z)	WeberE[\[Nu], - z] == - WeberE[- \[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
11.10.E13	${\displaystyle{\displaystyle\sin\left(\pi\nu\right)\,\mathbf{J}_{\nu}\left(z% \right)=\cos\left(\pi\nu\right)\,\mathbf{E}_{\nu}\left(z\right)-\mathbf{E}_{-% \nu}\left(z\right)}}$ `\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}`		sin(Pinu)AngerJ(nu, z) = cos(Pinu)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	${\displaystyle{\displaystyle\sin\left(\pi\nu\right)\,\mathbf{E}_{\nu}\left(z% \right)=\mathbf{J}_{-\nu}\left(z\right)-\cos\left(\pi\nu\right)\,\mathbf{J}_{% \nu}\left(z\right)}}$ `\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}`		sin(Pinu)WeberE(nu, z) = AngerJ(- nu, z)- cos(Pinu)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	${\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=\frac{\sin\left(\pi% \nu\right)}{\pi}(s_{{0},{\nu}}\left(z\right)-\nu s_{{-1},{\nu}}\left(z\right))}}$ `\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})`		AngerJ(nu, z) = (sin(Pinu))/(Pi)(LommelS1(0, nu, z)- nu*LommelS1(- 1, nu, z))	Error	Successful	Missing Macro Error	-	-
11.10.E18	${\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(z\right)=-\frac{1}{\pi}(1+% \cos\left(\pi\nu\right))s_{{0},{\nu}}\left(z\right)\\ -\frac{\nu}{\pi}(1-\cos\left(\pi\nu\right))s_{{-1},{\nu}}\left(z\right)}}$ `\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) = -(1)/(Pi)(1 + cos(Pinu))LommelS1(0, nu, z); -(nu)/(Pi)(1 - cos(Pinu))* LommelS1(- 1, nu, z)	Error	Successful	Missing Macro Error	-	-
11.10.E19	${\displaystyle{\displaystyle\mathbf{J}_{-\frac{1}{2}}\left(z\right)=\mathbf{E}% _{\frac{1}{2}}\left(z\right)\\ }}$ `\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\`		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	${\displaystyle{\displaystyle\mathbf{E}_{\frac{1}{2}}\left(z\right)\\ =(\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos z-A_{-}(\chi)\sin z)}}$ `\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})`		WeberE((1)/(2), z) = ((1)/(2)Piz)^(-(1)/(2))(A[+](chi) cos(z)- A[-](chi)* sin(z))	WeberE[Divide[1,2], z] == (Divide[1,2]Piz)^(-Divide[1,2])(Subscript[A, +][\[Chi]] Cos[z]- Subscript[A, -][\[Chi]]* Sin[z])	Error	Failure	-	Error
11.10.E20	${\displaystyle{\displaystyle\mathbf{J}_{\frac{1}{2}}\left(z\right)=-\mathbf{E}% _{-\frac{1}{2}}\left(z\right)\\ }}$ `\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\`		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	${\displaystyle{\displaystyle-\mathbf{E}_{-\frac{1}{2}}\left(z\right)\\ =(\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin z+A_{-}(\chi)\cos z)}}$ `-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})`		- WeberE(-(1)/(2), z) = ((1)/(2)Piz)^(-(1)/(2))(A[+](chi) sin(z)+ A[-](chi)* cos(z))	- WeberE[-Divide[1,2], z] == (Divide[1,2]Piz)^(-Divide[1,2])(Subscript[A, +][\[Chi]] Sin[z]+ Subscript[A, -][\[Chi]]* Cos[z])	Error	Failure	-	Error
11.10#Ex3	${\displaystyle{\displaystyle A_{+}(\chi)=C\left(\chi\right)+S\left(\chi\right)}}$ `A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}`		A[+](chi) = FresnelC(chi)+ FresnelS(chi)	Subscript[A, +][\[Chi]] == FresnelC[\[Chi]]+ FresnelS[\[Chi]]	Error	Failure	-	Error
11.10#Ex3	${\displaystyle{\displaystyle A_{-}(\chi)=C\left(\chi\right)-S\left(\chi\right)}}$ `A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}`		A[-](chi) = FresnelC(chi)- FresnelS(chi)	Subscript[A, -][\[Chi]] == FresnelC[\[Chi]]- FresnelS[\[Chi]]	Error	Failure	-	Error
11.10#Ex4	${\displaystyle{\displaystyle\chi=(2z/\pi)^{\frac{1}{2}}}}$ `\chi = (2z/\pi)^{\frac{1}{2}}`		chi = (2*z/Pi)^((1)/(2))	\[Chi] == (2*z/Pi)^(Divide[1,2])	Skipped - no semantic math	Skipped - no semantic math	-	-
11.10.E22	${\displaystyle{\displaystyle\mathbf{E}_{n}\left(z\right)=-\mathbf{H}_{n}\left(% z\right)+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\Gamma\left(k+\tfrac{1}{2}\right% )}{\Gamma\left(n\!+\!\tfrac{1}{2}\!-\!k\right)}(\tfrac{1}{2}z)^{n-2k-1}}}$ `\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}`	${\displaystyle{\displaystyle\Re(k+\tfrac{1}{2})>0,\Re(n+\tfrac{1}{2}-k)>0,\Re(% n+n+\tfrac{3}{2})>0}}$	WeberE(n, z) = - StruveH(n, z)+(1)/(Pi)sum((GAMMA(k +(1)/(2)))/(GAMMA(n +(1)/(2)- k))((1)/(2)z)^(n - 2k - 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 - 2k - 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	${\displaystyle{\displaystyle\mathbf{E}_{-n}\left(z\right)=-\mathbf{H}_{-n}% \left(z\right)+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\Gamma\left(n\!-% \!k\!-\!\tfrac{1}{2}\right)}{\Gamma\left(k+\tfrac{3}{2}\right)}(\tfrac{1}{2}z)% ^{-n+2k+1}}}$ `\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}`	${\displaystyle{\displaystyle\Re(n-k-\tfrac{1}{2})>0,\Re(k+\tfrac{3}{2})>0,\Re(% n+(-n)+\tfrac{3}{2})>0}}$	WeberE(- n, z) = - StruveH(- n, z)+((- 1)^(n + 1))/(Pi)sum((GAMMA(n - k -(1)/(2)))/(GAMMA(k +(3)/(2)))((1)/(2)z)^(- n + 2k + 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 + 2k + 1), {k, 0, Subscript[m, 2]}, GenerateConditions->None]	Failure	Failure	Failed [210 / 210] Result: -.5182370935+.1715162156I Test Values: {z = 1/23^(1/2)+1/2I, m[2] = 1/23^(1/2)+1/2I, n = 1} Result: .1977910573+.6179671328e-1I Test Values: {z = 1/23^(1/2)+1/2I, m[2] = 1/23^(1/2)+1/2I, 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	${\displaystyle{\displaystyle m_{1}=\left\lfloor\tfrac{1}{2}n-\tfrac{1}{2}% \right\rfloor}}$ `m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}`		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+.5000000000I Test Values: {m[1] = 1/23^(1/2)+1/2I, n = 1} Result: .8660254040+.5000000000I Test Values: {m[1] = 1/23^(1/2)+1/2I, 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	${\displaystyle{\displaystyle m_{2}=\left\lceil\tfrac{1}{2}n-\tfrac{3}{2}\right% \rceil}}$ `m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}`		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+.5000000000I Test Values: {m[2] = 1/23^(1/2)+1/2I, n = 1} Result: .8660254040+.5000000000I Test Values: {m[2] = 1/23^(1/2)+1/2I, 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	${\displaystyle{\displaystyle\displaystyle\mathbf{J}_{\nu}\left(0\right)=\frac{% \sin\left(\pi\nu\right)}{\pi\nu}}}$ `\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}`		AngerJ(nu, 0) = (sin(Pinu))/(Pinu)	AngerJ[\[Nu], 0] == Divide[Sin[Pi\[Nu]],Pi\[Nu]]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.10.E25	${\displaystyle{\displaystyle\displaystyle\mathbf{E}_{\nu}\left(0\right)=\frac{% 1-\cos\left(\pi\nu\right)}{\pi\nu}}}$ `\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}`		WeberE(nu, 0) = (1 - cos(Pinu))/(Pinu)	WeberE[\[Nu], 0] == Divide[1 - Cos[Pi\[Nu]],Pi\[Nu]]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.10.E26	${\displaystyle{\displaystyle\displaystyle\mathbf{E}_{0}\left(z\right)=-\mathbf% {H}_{0}\left(z\right)}}$ `\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}`	${\displaystyle{\displaystyle\Re(n+0+\tfrac{3}{2})>0}}$	WeberE(0, z) = - StruveH(0, z)	WeberE[0, z] == - StruveH[0, z]	Skipped - no semantic math	Skipped - no semantic math	-	-
11.10.E26	${\displaystyle{\displaystyle\displaystyle\mathbf{E}_{1}\left(z\right)=\frac{2}% {\pi}-\mathbf{H}_{1}\left(z\right)}}$ `\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}`	${\displaystyle{\displaystyle\Re(n+1+\tfrac{3}{2})>0}}$	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	${\displaystyle{\displaystyle\mathbf{J}_{n}\left(z\right)=J_{n}\left(z\right)}}$ `\AngerJ{n}@{z} = \BesselJ{n}@{z}`	${\displaystyle{\displaystyle\Re(n+k+1)>0}}$	AngerJ(n, z) = BesselJ(n, z)	AngerJ[n, z] == BesselJ[n, z]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
11.10.E32	${\displaystyle{\displaystyle\mathbf{J}_{\nu-1}\left(z\right)+\mathbf{J}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{J}_{\nu}\left(z\right)-\frac{2}{\pi z}% \sin\left(\pi\nu\right)}}$ `\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) = (2nu)/(z)AngerJ(nu, z)-(2)/(Piz)sin(Pi*nu)	AngerJ[\[Nu]- 1, z]+ AngerJ[\[Nu]+ 1, z] == Divide[2\[Nu],z]AngerJ[\[Nu], z]-Divide[2,Piz]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	${\displaystyle{\displaystyle\mathbf{E}_{\nu-1}\left(z\right)+\mathbf{E}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{E}_{\nu}\left(z\right)-\frac{2}{\pi z}(1% -\cos\left(\pi\nu\right))}}$ `\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) = (2nu)/(z)WeberE(nu, z)-(2)/(Piz)(1 - cos(Pi*nu))	WeberE[\[Nu]- 1, z]+ WeberE[\[Nu]+ 1, z] == Divide[2\[Nu],z]WeberE[\[Nu], z]-Divide[2,Piz](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	${\displaystyle{\displaystyle 2\mathbf{J}_{\nu}'\left(z\right)=\mathbf{J}_{\nu-% 1}\left(z\right)-\mathbf{J}_{\nu+1}\left(z\right)}}$ `2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}`		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	${\displaystyle{\displaystyle 2\mathbf{E}_{\nu}'\left(z\right)=\mathbf{E}_{\nu-% 1}\left(z\right)-\mathbf{E}_{\nu+1}\left(z\right)}}$ `2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}`		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	${\displaystyle{\displaystyle z\mathbf{J}_{\nu}'\left(z\right)+\nu\mathbf{J}_{% \nu}\left(z\right)=+z\mathbf{J}_{\nu-1}\left(z\right)+\frac{\sin\left(\pi\nu% \right)}{\pi}}}$ `z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}`		zdiff( AngerJ(nu, z), z$(1) )+ nuAngerJ(nu, z) = + zAngerJ(nu - 1, z)+(sin(Pinu))/(Pi)	zD[AngerJ[\[Nu], z], {z, 1}]+ \[Nu]AngerJ[\[Nu], z] == + zAngerJ[\[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	${\displaystyle{\displaystyle z\mathbf{J}_{\nu}'\left(z\right)-\nu\mathbf{J}_{% \nu}\left(z\right)=-z\mathbf{J}_{\nu+1}\left(z\right)-\frac{\sin\left(\pi\nu% \right)}{\pi}}}$ `z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}`		zdiff( AngerJ(nu, z), z$(1) )- nuAngerJ(nu, z) = - zAngerJ(nu + 1, z)-(sin(Pinu))/(Pi)	zD[AngerJ[\[Nu], z], {z, 1}]- \[Nu]AngerJ[\[Nu], z] == - zAngerJ[\[Nu]+ 1, z]-Divide[Sin[Pi\[Nu]],Pi]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 70]
11.10.E37	${\displaystyle{\displaystyle z\mathbf{E}_{\nu}'\left(z\right)+\nu\mathbf{E}_{% \nu}\left(z\right)=+z\mathbf{E}_{\nu-1}\left(z\right)+\frac{(1-\cos\left(\pi% \nu\right))}{\pi}}}$ `z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}`		zdiff( WeberE(nu, z), z$(1) )+ nuWeberE(nu, z) = + zWeberE(nu - 1, z)+(1 - cos(Pinu))/(Pi)	zD[WeberE[\[Nu], z], {z, 1}]+ \[Nu]WeberE[\[Nu], z] == + zWeberE[\[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	${\displaystyle{\displaystyle z\mathbf{E}_{\nu}'\left(z\right)-\nu\mathbf{E}_{% \nu}\left(z\right)=-z\mathbf{E}_{\nu+1}\left(z\right)-\frac{(1-\cos\left(\pi% \nu\right))}{\pi}}}$ `z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}`		zdiff( WeberE(nu, z), z$(1) )- nuWeberE(nu, z) = - zWeberE(nu + 1, z)-(1 - cos(Pinu))/(Pi)	zD[WeberE[\[Nu], z], {z, 1}]- \[Nu]WeberE[\[Nu], z] == - zWeberE[\[Nu]+ 1, z]-Divide[1 - Cos[Pi\[Nu]],Pi]	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 70]

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/11.10.E1 11.10.E1] || [[Item:Q4018|<math>\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 70] || Skipped - Because timed out
+| [https://dlmf.nist.gov/11.10.E1 11.10.E1] || <math qid="Q4018">\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 70] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/11.10.E2 11.10.E2] || [[Item:Q4019|<math>\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = (1)/(Pi)*int(sin(nu*theta - z*sin(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 70] || Skipped - Because timed out
+| [https://dlmf.nist.gov/11.10.E2 11.10.E2] || <math qid="Q4019">\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{\nu\theta-z\sin@@{\theta}}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = (1)/(Pi)*int(sin(nu*theta - z*sin(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 70] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/11.10.E3 11.10.E3] || [[Item:Q4020|<math>\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}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || Successful [Tested: 70] || Skipped - Because timed out
+| [https://dlmf.nist.gov/11.10.E3 11.10.E3] || <math qid="Q4020">\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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || Successful [Tested: 70] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/11.10.E8 11.10.E8] || [[Item:Q4025|<math>\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = cos((1)/(2)*Pi*nu)*S[1](nu , z)+ sin((1)/(2)*Pi*nu)*S[2](nu , z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4325617835-.4216939044*I-(1.695493166+.2075033380*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
+| [https://dlmf.nist.gov/11.10.E8 11.10.E8] || <math qid="Q4025">\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \cos@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)+\sin@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = cos((1)/(2)*Pi*nu)*S[1](nu , z)+ sin((1)/(2)*Pi*nu)*S[2](nu , z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
 |-
-| [https://dlmf.nist.gov/11.10.E9 11.10.E9] || [[Item:Q4026|<math>\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = sin((1)/(2)*Pi*nu)*S[1](nu , z)- cos((1)/(2)*Pi*nu)*S[2](nu , z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6530158617-.8867638354e-1*I-(.3667170623+1.402184312*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)
+| [https://dlmf.nist.gov/11.10.E9 11.10.E9] || <math qid="Q4026">\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{z} = \sin@{\tfrac{1}{2}\pi\nu}\,S_{1}(\nu,z)-\cos@{\tfrac{1}{2}\pi\nu}\,S_{2}(\nu,z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = sin((1)/(2)*Pi*nu)*S[1](nu , z)- cos((1)/(2)*Pi*nu)*S[2](nu , z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
 |-
-| [https://dlmf.nist.gov/11.10.E10 11.10.E10] || [[Item:Q4027|<math>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}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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}}</syntaxhighlight> || <math>\realpart@@{(k+\tfrac{1}{2}\nu+1)} > 0, \realpart@@{(k-\tfrac{1}{2}\nu+1)} > 0</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.6234597010+.4805214665*I
+| [https://dlmf.nist.gov/11.10.E10 11.10.E10] || <math qid="Q4027">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}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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}}</syntaxhighlight> || <math>\realpart@@{(k+\tfrac{1}{2}\nu+1)} > 0, \realpart@@{(k-\tfrac{1}{2}\nu+1)} > 0</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
 |-
-| [https://dlmf.nist.gov/11.10.E11 11.10.E11] || [[Item:Q4028|<math>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}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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}}}</syntaxhighlight> || <math>\realpart@@{(k+\tfrac{1}{2}\nu+\tfrac{3}{2})} > 0, \realpart@@{(k-\tfrac{1}{2}\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, .8660254040+.5000000000*I)-.4892722811e-1+.1117224133*I
+| [https://dlmf.nist.gov/11.10.E11 11.10.E11] || <math qid="Q4028">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}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>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}}}</syntaxhighlight> || <math>\realpart@@{(k+\tfrac{1}{2}\nu+\tfrac{3}{2})} > 0, \realpart@@{(k-\tfrac{1}{2}\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
 |-
-| [https://dlmf.nist.gov/11.10#Ex1 11.10#Ex1] || [[Item:Q4029|<math>\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, - z) = AngerJ(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], - z] == AngerJ[- \[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.10#Ex1 11.10#Ex1] || <math qid="Q4029">\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{-z} = \AngerJ{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, - z) = AngerJ(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu], - z] == AngerJ[- \[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10#Ex2 11.10#Ex2] || [[Item:Q4030|<math>\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, - z) = - WeberE(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], - z] == - WeberE[- \[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.10#Ex2 11.10#Ex2] || <math qid="Q4030">\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu}@{-z} = -\WeberE{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, - z) = - WeberE(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu], - z] == - WeberE[- \[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E13 11.10.E13] || [[Item:Q4031|<math>\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(Pi*nu)*AngerJ(nu, z) = cos(Pi*nu)*WeberE(nu, z)- WeberE(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Pi*\[Nu]]*AngerJ[\[Nu], z] == Cos[Pi*\[Nu]]*WeberE[\[Nu], z]- WeberE[- \[Nu], z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.10.E13 11.10.E13] || <math qid="Q4031">\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\pi\nu}\,\AngerJ{\nu}@{z} = \cos@{\pi\nu}\,\WeberE{\nu}@{z}-\WeberE{-\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(Pi*nu)*AngerJ(nu, z) = cos(Pi*nu)*WeberE(nu, z)- WeberE(- nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Pi*\[Nu]]*AngerJ[\[Nu], z] == Cos[Pi*\[Nu]]*WeberE[\[Nu], z]- WeberE[- \[Nu], z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E14 11.10.E14] || [[Item:Q4032|<math>\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(Pi*nu)*WeberE(nu, z) = AngerJ(- nu, z)- cos(Pi*nu)*AngerJ(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Pi*\[Nu]]*WeberE[\[Nu], z] == AngerJ[- \[Nu], z]- Cos[Pi*\[Nu]]*AngerJ[\[Nu], z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.10.E14 11.10.E14] || <math qid="Q4032">\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\pi\nu}\,\WeberE{\nu}@{z} = \AngerJ{-\nu}@{z}-\cos@{\pi\nu}\,\AngerJ{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(Pi*nu)*WeberE(nu, z) = AngerJ(- nu, z)- cos(Pi*nu)*AngerJ(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Pi*\[Nu]]*WeberE[\[Nu], z] == AngerJ[- \[Nu], z]- Cos[Pi*\[Nu]]*AngerJ[\[Nu], z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E17 11.10.E17] || [[Item:Q4035|<math>\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = (sin(Pi*nu))/(Pi)*(LommelS1(0, nu, z)- nu*LommelS1(- 1, nu, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
+| [https://dlmf.nist.gov/11.10.E17 11.10.E17] || <math qid="Q4035">\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu}@{z} = \frac{\sin@{\pi\nu}}{\pi}(\Lommels{0}{\nu}@{z}-\nu\Lommels{-1}{\nu}@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu, z) = (sin(Pi*nu))/(Pi)*(LommelS1(0, nu, z)- nu*LommelS1(- 1, nu, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
 |-
-| [https://dlmf.nist.gov/11.10.E18 11.10.E18] || [[Item:Q4036|<math>\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}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = -(1)/(Pi)*(1 + cos(Pi*nu))*LommelS1(0, nu, z)*; -(nu)/(Pi)*(1 - cos(Pi*nu))* LommelS1(- 1, nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
+| [https://dlmf.nist.gov/11.10.E18 11.10.E18] || <math qid="Q4036">\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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu, z) = -(1)/(Pi)*(1 + cos(Pi*nu))*LommelS1(0, nu, z)*; -(nu)/(Pi)*(1 - cos(Pi*nu))* LommelS1(- 1, nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
 |-
-| [https://dlmf.nist.gov/11.10.E19 11.10.E19] || [[Item:Q4037|<math>\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(-(1)/(2), z) = WeberE((1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[-Divide[1,2], z] == WeberE[Divide[1,2], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/11.10.E19 11.10.E19] || <math qid="Q4037">\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{-\frac{1}{2}}@{z} = \WeberE{\frac{1}{2}}@{z}\\</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(-(1)/(2), z) = WeberE((1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[-Divide[1,2], z] == WeberE[Divide[1,2], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/11.10.E19 11.10.E19] || [[Item:Q4037|<math>\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE((1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* cos(z)- A[-](chi)* sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Cos[z]- Subscript[A, -][\[Chi]]* Sin[z])</syntaxhighlight> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/11.10.E19 11.10.E19] || <math qid="Q4037">\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\cos@@{z}-A_{-}(\chi)\sin@@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE((1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* cos(z)- A[-](chi)* sin(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Cos[z]- Subscript[A, -][\[Chi]]* Sin[z])</syntaxhighlight> || Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/11.10.E20 11.10.E20] || [[Item:Q4038|<math>\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ((1)/(2), z) = - WeberE(-(1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[Divide[1,2], z] == - WeberE[-Divide[1,2], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/11.10.E20 11.10.E20] || <math qid="Q4038">\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\frac{1}{2}}@{z} = -\WeberE{-\frac{1}{2}}@{z}\\</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ((1)/(2), z) = - WeberE(-(1)/(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[Divide[1,2], z] == - WeberE[-Divide[1,2], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/11.10.E20 11.10.E20] || [[Item:Q4038|<math>-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- WeberE(-(1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* sin(z)+ A[-](chi)* cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- WeberE[-Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Sin[z]+ Subscript[A, -][\[Chi]]* Cos[z])</syntaxhighlight> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/11.10.E20 11.10.E20] || <math qid="Q4038">-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\WeberE{-\frac{1}{2}}@{z}\\ = (\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin@@{z}+A_{-}(\chi)\cos@@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- WeberE(-(1)/(2), z) = ((1)/(2)*Pi*z)^(-(1)/(2))*(A[+](chi)* sin(z)+ A[-](chi)* cos(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- WeberE[-Divide[1,2], z] == (Divide[1,2]*Pi*z)^(-Divide[1,2])*(Subscript[A, +][\[Chi]]* Sin[z]+ Subscript[A, -][\[Chi]]* Cos[z])</syntaxhighlight> || Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/11.10#Ex3 11.10#Ex3] || [[Item:Q4039|<math>A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[+](chi) = FresnelC(chi)+ FresnelS(chi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, +][\[Chi]] == FresnelC[\[Chi]]+ FresnelS[\[Chi]]</syntaxhighlight> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/11.10#Ex3 11.10#Ex3] || <math qid="Q4039">A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{+}(\chi) = \Fresnelcosint@{\chi}+\Fresnelsinint@{\chi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[+](chi) = FresnelC(chi)+ FresnelS(chi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, +][\[Chi]] == FresnelC[\[Chi]]+ FresnelS[\[Chi]]</syntaxhighlight> || Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/11.10#Ex3 11.10#Ex3] || [[Item:Q4039|<math>A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[-](chi) = FresnelC(chi)- FresnelS(chi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, -][\[Chi]] == FresnelC[\[Chi]]- FresnelS[\[Chi]]</syntaxhighlight> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/11.10#Ex3 11.10#Ex3] || <math qid="Q4039">A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{-}(\chi) = \Fresnelcosint@{\chi}-\Fresnelsinint@{\chi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[-](chi) = FresnelC(chi)- FresnelS(chi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, -][\[Chi]] == FresnelC[\[Chi]]- FresnelS[\[Chi]]</syntaxhighlight> || Error || Failure || - || Error
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/11.10#Ex4 11.10#Ex4] || [[Item:Q4040|<math>\chi = (2z/\pi)^{\frac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\chi = (2z/\pi)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">chi = (2*z/Pi)^((1)/(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Chi] == (2*z/Pi)^(Divide[1,2])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/11.10#Ex4 11.10#Ex4] || <math qid="Q4040">\chi = (2z/\pi)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\chi = (2z/\pi)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">chi = (2*z/Pi)^((1)/(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Chi] == (2*z/Pi)^(Divide[1,2])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/11.10.E22 11.10.E22] || [[Item:Q4041|<math>\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}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math>\realpart@@{(k+\tfrac{1}{2})} > 0, \realpart@@{(n+\tfrac{1}{2}-k)} > 0, \realpart@@{(n+n+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.6366197723675814, Times[-0.3183098861837907, DifferenceRoot[Function[{, }
+| [https://dlmf.nist.gov/11.10.E22 11.10.E22] || <math qid="Q4041">\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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math>\realpart@@{(k+\tfrac{1}{2})} > 0, \realpart@@{(n+\tfrac{1}{2}-k)} > 0, \realpart@@{(n+n+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.10.E23 11.10.E23] || [[Item:Q4042|<math>\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}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math>\realpart@@{(n-k-\tfrac{1}{2})} > 0, \realpart@@{(k+\tfrac{3}{2})} > 0, \realpart@@{(n+(-n)+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5182370935+.1715162156*I
+| [https://dlmf.nist.gov/11.10.E23 11.10.E23] || <math qid="Q4042">\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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\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}</syntaxhighlight> || <math>\realpart@@{(n-k-\tfrac{1}{2})} > 0, \realpart@@{(k+\tfrac{3}{2})} > 0, \realpart@@{(n+(-n)+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5182370936641069, 0.17151621559870867]
@@ Line 72: / Line 72: @@
 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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.10#Ex5 11.10#Ex5] || [[Item:Q4043|<math>m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>m[1] = floor((1)/(2)*n -(1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[m, 1] == Floor[Divide[1,2]*n -Divide[1,2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
+| [https://dlmf.nist.gov/11.10#Ex5 11.10#Ex5] || <math qid="Q4043">m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>m_{1} = \floor{\tfrac{1}{2}n-\tfrac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>m[1] = floor((1)/(2)*n -(1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[m, 1] == Floor[Divide[1,2]*n -Divide[1,2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
 Test Values: {m[1] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
 Test Values: {m[1] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
@@ Line 78: / Line 78: @@
 Test Values: {Rule[n, 2], Rule[Subscript[m, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.10#Ex6 11.10#Ex6] || [[Item:Q4044|<math>m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>m[2] = ceil((1)/(2)*n -(3)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[m, 2] == Ceiling[Divide[1,2]*n -Divide[3,2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.866025404+.5000000000*I
+| [https://dlmf.nist.gov/11.10#Ex6 11.10#Ex6] || <math qid="Q4044">m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>m_{2} = \ceiling{\tfrac{1}{2}n-\tfrac{3}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>m[2] = ceil((1)/(2)*n -(3)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[m, 2] == Ceiling[Divide[1,2]*n -Divide[3,2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.866025404+.5000000000*I
 Test Values: {m[2] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
 Test Values: {m[2] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.8660254037844388, 0.49999999999999994]
@@ Line 84: / Line 84: @@
 Test Values: {Rule[n, 2], Rule[Subscript[m, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/11.10.E25 11.10.E25] || [[Item:Q4046|<math>\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">AngerJ(nu, 0) = (sin(Pi*nu))/(Pi*nu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">AngerJ[\[Nu], 0] == Divide[Sin[Pi*\[Nu]],Pi*\[Nu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/11.10.E25 11.10.E25] || <math qid="Q4046">\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\AngerJ{\nu}@{0} = \frac{\sin@{\pi\nu}}{\pi\nu}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">AngerJ(nu, 0) = (sin(Pi*nu))/(Pi*nu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">AngerJ[\[Nu], 0] == Divide[Sin[Pi*\[Nu]],Pi*\[Nu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/11.10.E25 11.10.E25] || [[Item:Q4046|<math>\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE(nu, 0) = (1 - cos(Pi*nu))/(Pi*nu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE[\[Nu], 0] == Divide[1 - Cos[Pi*\[Nu]],Pi*\[Nu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/11.10.E25 11.10.E25] || <math qid="Q4046">\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\WeberE{\nu}@{0} = \frac{1-\cos@{\pi\nu}}{\pi\nu}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE(nu, 0) = (1 - cos(Pi*nu))/(Pi*nu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE[\[Nu], 0] == Divide[1 - Cos[Pi*\[Nu]],Pi*\[Nu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/11.10.E26 11.10.E26] || [[Item:Q4048|<math>\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}</syntaxhighlight> || <math>\realpart@@{(n+0+\tfrac{3}{2})} > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE(0, z) = - StruveH(0, z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE[0, z] == - StruveH[0, z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/11.10.E26 11.10.E26] || <math qid="Q4048">\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\WeberE{0}@{z} = -\StruveH{0}@{z}</syntaxhighlight> || <math>\realpart@@{(n+0+\tfrac{3}{2})} > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE(0, z) = - StruveH(0, z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE[0, z] == - StruveH[0, z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/11.10.E26 11.10.E26] || [[Item:Q4048|<math>\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</syntaxhighlight> || <math>\realpart@@{(n+1+\tfrac{3}{2})} > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE(1, z) = (2)/(Pi)- StruveH(1, z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE[1, z] == Divide[2,Pi]- StruveH[1, z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/11.10.E26 11.10.E26] || <math qid="Q4048">\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\WeberE{1}@{z} = \frac{2}{\pi}-\StruveH{1}@{z}</syntaxhighlight> || <math>\realpart@@{(n+1+\tfrac{3}{2})} > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE(1, z) = (2)/(Pi)- StruveH(1, z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">WeberE[1, z] == Divide[2,Pi]- StruveH[1, z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/11.10.E29 11.10.E29] || [[Item:Q4051|<math>\AngerJ{n}@{z} = \BesselJ{n}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{n}@{z} = \BesselJ{n}@{z}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>AngerJ(n, z) = BesselJ(n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[n, z] == BesselJ[n, z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/11.10.E29 11.10.E29] || <math qid="Q4051">\AngerJ{n}@{z} = \BesselJ{n}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{n}@{z} = \BesselJ{n}@{z}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>AngerJ(n, z) = BesselJ(n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[n, z] == BesselJ[n, z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/11.10.E32 11.10.E32] || [[Item:Q4054|<math>\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu - 1, z)+ AngerJ(nu + 1, z) = (2*nu)/(z)*AngerJ(nu, z)-(2)/(Pi*z)*sin(Pi*nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu]- 1, z]+ AngerJ[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*AngerJ[\[Nu], z]-Divide[2,Pi*z]*Sin[Pi*\[Nu]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1812319651
+| [https://dlmf.nist.gov/11.10.E32 11.10.E32] || <math qid="Q4054">\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AngerJ{\nu-1}@{z}+\AngerJ{\nu+1}@{z} = \frac{2\nu}{z}\AngerJ{\nu}@{z}-\frac{2}{\pi z}\sin@{\pi\nu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>AngerJ(nu - 1, z)+ AngerJ(nu + 1, z) = (2*nu)/(z)*AngerJ(nu, z)-(2)/(Pi*z)*sin(Pi*nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>AngerJ[\[Nu]- 1, z]+ AngerJ[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*AngerJ[\[Nu], z]-Divide[2,Pi*z]*Sin[Pi*\[Nu]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1812319651
 Test Values: {nu = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1208213102
 Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E33 11.10.E33] || [[Item:Q4055|<math>\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu - 1, z)+ WeberE(nu + 1, z) = (2*nu)/(z)*WeberE(nu, z)-(2)/(Pi*z)*(1 - cos(Pi*nu))</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu]- 1, z]+ WeberE[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*WeberE[\[Nu], z]-Divide[2,Pi*z]*(1 - Cos[Pi*\[Nu]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1812319648
+| [https://dlmf.nist.gov/11.10.E33 11.10.E33] || <math qid="Q4055">\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\WeberE{\nu-1}@{z}+\WeberE{\nu+1}@{z} = \frac{2\nu}{z}\WeberE{\nu}@{z}-\frac{2}{\pi z}(1-\cos@{\pi\nu})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>WeberE(nu - 1, z)+ WeberE(nu + 1, z) = (2*nu)/(z)*WeberE(nu, z)-(2)/(Pi*z)*(1 - cos(Pi*nu))</syntaxhighlight> || <syntaxhighlight lang=mathematica>WeberE[\[Nu]- 1, z]+ WeberE[\[Nu]+ 1, z] == Divide[2*\[Nu],z]*WeberE[\[Nu], z]-Divide[2,Pi*z]*(1 - Cos[Pi*\[Nu]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1812319648
 Test Values: {nu = 3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1812319652
 Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E34 11.10.E34] || [[Item:Q4056|<math>2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*diff( AngerJ(nu, z), z$(1) ) = AngerJ(nu - 1, z)- AngerJ(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*D[AngerJ[\[Nu], z], {z, 1}] == AngerJ[\[Nu]- 1, z]- AngerJ[\[Nu]+ 1, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1812319651
+| [https://dlmf.nist.gov/11.10.E34 11.10.E34] || <math qid="Q4056">2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\AngerJ{\nu}'@{z} = \AngerJ{\nu-1}@{z}-\AngerJ{\nu+1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*diff( AngerJ(nu, z), z$(1) ) = AngerJ(nu - 1, z)- AngerJ(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*D[AngerJ[\[Nu], z], {z, 1}] == AngerJ[\[Nu]- 1, z]- AngerJ[\[Nu]+ 1, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1812319651
 Test Values: {nu = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1208213102
 Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E35 11.10.E35] || [[Item:Q4057|<math>2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*diff( WeberE(nu, z), z$(1) ) = WeberE(nu - 1, z)- WeberE(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*D[WeberE[\[Nu], z], {z, 1}] == WeberE[\[Nu]- 1, z]- WeberE[\[Nu]+ 1, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1812319648
+| [https://dlmf.nist.gov/11.10.E35 11.10.E35] || <math qid="Q4057">2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\WeberE{\nu}'@{z} = \WeberE{\nu-1}@{z}-\WeberE{\nu+1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*diff( WeberE(nu, z), z$(1) ) = WeberE(nu - 1, z)- WeberE(nu + 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*D[WeberE[\[Nu], z], {z, 1}] == WeberE[\[Nu]- 1, z]- WeberE[\[Nu]+ 1, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1812319648
 Test Values: {nu = 3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1812319652
 Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E36 11.10.E36] || [[Item:Q4058|<math>z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( AngerJ(nu, z), z$(1) )+ nu*AngerJ(nu, z) = + z*AngerJ(nu - 1, z)+(sin(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[AngerJ[\[Nu], z], {z, 1}]+ \[Nu]*AngerJ[\[Nu], z] == + z*AngerJ[\[Nu]- 1, z]+Divide[Sin[Pi*\[Nu]],Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2718479477
+| [https://dlmf.nist.gov/11.10.E36 11.10.E36] || <math qid="Q4058">z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\AngerJ{\nu}'@{z}+\nu\AngerJ{\nu}@{z} = + z\AngerJ{\nu- 1}@{z}+\frac{\sin@{\pi\nu}}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( AngerJ(nu, z), z$(1) )+ nu*AngerJ(nu, z) = + z*AngerJ(nu - 1, z)+(sin(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[AngerJ[\[Nu], z], {z, 1}]+ \[Nu]*AngerJ[\[Nu], z] == + z*AngerJ[\[Nu]- 1, z]+Divide[Sin[Pi*\[Nu]],Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2718479477
 Test Values: {nu = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1812319655
 Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E36 11.10.E36] || [[Item:Q4058|<math>z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( AngerJ(nu, z), z$(1) )- nu*AngerJ(nu, z) = - z*AngerJ(nu + 1, z)-(sin(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[AngerJ[\[Nu], z], {z, 1}]- \[Nu]*AngerJ[\[Nu], z] == - z*AngerJ[\[Nu]+ 1, z]-Divide[Sin[Pi*\[Nu]],Pi]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.10.E36 11.10.E36] || <math qid="Q4058">z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\AngerJ{\nu}'@{z}-\nu\AngerJ{\nu}@{z} = - z\AngerJ{\nu+ 1}@{z}-\frac{\sin@{\pi\nu}}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( AngerJ(nu, z), z$(1) )- nu*AngerJ(nu, z) = - z*AngerJ(nu + 1, z)-(sin(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[AngerJ[\[Nu], z], {z, 1}]- \[Nu]*AngerJ[\[Nu], z] == - z*AngerJ[\[Nu]+ 1, z]-Divide[Sin[Pi*\[Nu]],Pi]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E37 11.10.E37] || [[Item:Q4059|<math>z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( WeberE(nu, z), z$(1) )+ nu*WeberE(nu, z) = + z*WeberE(nu - 1, z)+(1 - cos(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[WeberE[\[Nu], z], {z, 1}]+ \[Nu]*WeberE[\[Nu], z] == + z*WeberE[\[Nu]- 1, z]+Divide[1 - Cos[Pi*\[Nu]],Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2718479477
+| [https://dlmf.nist.gov/11.10.E37 11.10.E37] || <math qid="Q4059">z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\WeberE{\nu}'@{z}+\nu\WeberE{\nu}@{z} = + z\WeberE{\nu- 1}@{z}+\frac{(1-\cos@{\pi\nu})}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( WeberE(nu, z), z$(1) )+ nu*WeberE(nu, z) = + z*WeberE(nu - 1, z)+(1 - cos(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[WeberE[\[Nu], z], {z, 1}]+ \[Nu]*WeberE[\[Nu], z] == + z*WeberE[\[Nu]- 1, z]+Divide[1 - Cos[Pi*\[Nu]],Pi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2718479477
 Test Values: {nu = 3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2718479472
 Test Values: {nu = -1/2, z = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.10.E37 11.10.E37] || [[Item:Q4059|<math>z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( WeberE(nu, z), z$(1) )- nu*WeberE(nu, z) = - z*WeberE(nu + 1, z)-(1 - cos(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[WeberE[\[Nu], z], {z, 1}]- \[Nu]*WeberE[\[Nu], z] == - z*WeberE[\[Nu]+ 1, z]-Divide[1 - Cos[Pi*\[Nu]],Pi]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.10.E37 11.10.E37] || <math qid="Q4059">z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\WeberE{\nu}'@{z}-\nu\WeberE{\nu}@{z} = - z\WeberE{\nu+ 1}@{z}-\frac{(1-\cos@{\pi\nu})}{\pi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff( WeberE(nu, z), z$(1) )- nu*WeberE(nu, z) = - z*WeberE(nu + 1, z)-(1 - cos(Pi*nu))/(Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[WeberE[\[Nu], z], {z, 1}]- \[Nu]*WeberE[\[Nu], z] == - z*WeberE[\[Nu]+ 1, z]-Divide[1 - Cos[Pi*\[Nu]],Pi]</syntaxhighlight> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 70]
 |}
 </div>

11.10: Difference between revisions

Latest revision as of 11:29, 28 June 2021

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