11.2: Difference between revisions

Latest revision as of 11:28, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
11.2.E1	${\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=(\tfrac{1}{2}z)^{% \nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\Gamma\left(n+% \tfrac{3}{2}\right)\Gamma\left(n+\nu+\tfrac{3}{2}\right)}}}$ `\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}`	${\displaystyle{\displaystyle\Re(n+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	StruveH(nu, z) = ((1)/(2)z)^(nu + 1) sum(((- 1)^(n)((1)/(2)z)^(2n))/(GAMMA(n +(3)/(2))GAMMA(n + nu +(3)/(2))), n = 0..infinity)	StruveH[\[Nu], z] == (Divide[1,2]z)^(\[Nu]+ 1) Sum[Divide[(- 1)^(n)(Divide[1,2]z)^(2n),Gamma[n +Divide[3,2]]Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 70]
11.2.E2	${\displaystyle{\displaystyle\mathbf{L}_{\nu}\left(z\right)=-ie^{-\frac{1}{2}% \pi i\nu}\mathbf{H}_{\nu}\left(iz\right)}}$ `\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}`	${\displaystyle{\displaystyle\Re(n+\nu+\tfrac{3}{2})>0}}$	StruveL(nu, z) = - Iexp(-(1)/(2)PiInu)StruveH(nu, Iz)	StruveL[\[Nu], z] == - IExp[-Divide[1,2]PiI\[Nu]]StruveH[\[Nu], Iz]	Failure	Failure	Failed [8 / 70] Result: 1.240284959+1.629557917I Test Values: {nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: 33.65868914+29.08337177I Test Values: {nu = -1/2+1/2I3^(1/2), z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [8 / 70] Result: Complex[1.2402849561066787, 1.6295579188731661] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[33.658689094091635, 29.08337174056143] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E2	${\displaystyle{\displaystyle-ie^{-\frac{1}{2}\pi i\nu}\mathbf{H}_{\nu}\left(iz% \right)=(\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{% \Gamma\left(n+\tfrac{3}{2}\right)\Gamma\left(n+\nu+\tfrac{3}{2}\right)}}}$ `-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}`	${\displaystyle{\displaystyle\Re(n+\nu+\tfrac{3}{2})>0,\Re(n+\tfrac{3}{2})>0}}$	- Iexp(-(1)/(2)PiInu)StruveH(nu, Iz) = ((1)/(2)z)^(nu + 1) sum((((1)/(2)z)^(2n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)	- IExp[-Divide[1,2]PiI\[Nu]]StruveH[\[Nu], Iz] == (Divide[1,2]z)^(\[Nu]+ 1) Sum[Divide[(Divide[1,2]z)^(2n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [8 / 70] Result: -1.240284959-1.629557917I Test Values: {nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} Result: -33.65868914-29.08337177I Test Values: {nu = -1/2+1/2I3^(1/2), z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [8 / 70] Result: Complex[-1.2402849561066787, -1.6295579188731661] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-33.658689094091635, -29.08337174056143] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E5	${\displaystyle{\displaystyle\mathbf{K}_{\nu}\left(z\right)=\mathbf{H}_{\nu}% \left(z\right)-Y_{\nu}\left(z\right)}}$ `\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re((-\nu)+k+1)>0,\Re(n+\nu+\tfrac{% 3}{2})>0}}$	StruveH(nu, z) - BesselY(nu, z) = StruveH(nu, z)- BesselY(nu, z)	StruveH[\[Nu], z] - BesselY[\[Nu], z] == StruveH[\[Nu], z]- BesselY[\[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
11.2.E6	${\displaystyle{\displaystyle\mathbf{M}_{\nu}\left(z\right)=\mathbf{L}_{\nu}% \left(z\right)-I_{\nu}\left(z\right)}}$ `\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	StruveL(nu, z) - BesselI(nu, z) = StruveL(nu, z)- BesselI(nu, z)	StruveL[\[Nu], z] - BesselI[\[Nu], z] == StruveL[\[Nu], z]- BesselI[\[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
11.2.E7	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\frac{% 1}{z}\frac{\mathrm{d}w}{\mathrm{d}z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w=% \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}}}$ `\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}`	${\displaystyle{\displaystyle\Re(\nu+\tfrac{1}{2})>0}}$	diff(w, [z$(2)])+(1)/(z)diff(w, z)+(1 -((nu)^(2))/((z)^(2)))w = (((1)/(2)z)^(nu - 1))/(sqrt(Pi)GAMMA(nu +(1)/(2)))	D[w, {z, 2}]+Divide[1,z]D[w, z]+(1 -Divide[\[Nu]^(2),(z)^(2)])w == Divide[(Divide[1,2]z)^(\[Nu]- 1),Sqrt[Pi]Gamma[\[Nu]+Divide[1,2]]]	Failure	Failure	Failed [300 / 300] Result: -.5630887369+.2307852889I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: 1.502962248+1.156533180I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.563088736999922, 0.23078528896155245] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.3603758852198513, 0.9342077190875079] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
11.2.E8	${\displaystyle{\displaystyle w=\mathbf{H}_{\nu}\left(z\right),\mathbf{K}_{\nu}% \left(z\right)}}$ `w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}`	${\displaystyle{\displaystyle\Re(n+\nu+\tfrac{3}{2})>0,\Re(\nu+k+1)>0,\Re((-\nu% )+k+1)>0}}$	w = StruveH(nu, z); StruveH(nu, z) - BesselY(nu, z)	w == StruveH[\[Nu], z] StruveH[\[Nu], z] - BesselY[\[Nu], z]	Failure	Failure	Error	Error
11.2.E9	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\frac{% 1}{z}\frac{\mathrm{d}w}{\mathrm{d}z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w=% \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}}}$ `\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}`	${\displaystyle{\displaystyle\Re(\nu+\tfrac{1}{2})>0}}$	diff(w, [z$(2)])+(1)/(z)diff(w, z)-(1 +((nu)^(2))/((z)^(2)))w = (((1)/(2)z)^(nu - 1))/(sqrt(Pi)GAMMA(nu +(1)/(2)))	D[w, {z, 2}]+Divide[1,z]D[w, z]-(1 +Divide[\[Nu]^(2),(z)^(2)])w == Divide[(Divide[1,2]z)^(\[Nu]- 1),Sqrt[Pi]Gamma[\[Nu]+Divide[1,2]]]	Failure	Failure	Failed [300 / 300] Result: -2.295139545-.7692147111I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -.2290885595+.1565331804I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-2.2951395445687996, -0.7692147110384474] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.0924266927887287, -0.06579228091249201] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
11.2.E10	${\displaystyle{\displaystyle w=\mathbf{L}_{\nu}\left(z\right),\mathbf{M}_{\nu}% \left(z\right)}}$ `w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	w = StruveL(nu, z); StruveL(nu, z) - BesselI(nu, z)	w == StruveL[\[Nu], z] StruveL[\[Nu], z] - BesselI[\[Nu], z]	Failure	Failure	Error	Error
11.2.E11	${\displaystyle{\displaystyle w=\mathbf{H}_{\nu}\left(x\right)+AJ_{\nu}\left(x% \right)+BY_{\nu}\left(x\right)}}$ `w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re((-\nu)+k+1)>0,\Re(n+\nu+\tfrac{% 3}{2})>0}}$	w = StruveH(nu, x)+ ABesselJ(nu, x)+ BBesselY(nu, x)	w == StruveH[\[Nu], x]+ ABesselJ[\[Nu], x]+ BBesselY[\[Nu], x]	Failure	Failure	Failed [300 / 300] Result: -.568729179e-1+1.004857129I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 3/2} Result: 1.306236381+1.613216681I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 1/2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.056872918319905263, 1.0048571288175818] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.7531990546092198, -1.6096988531229037] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E12	${\displaystyle{\displaystyle w=\mathbf{K}_{\nu}\left(x\right)+AJ_{\nu}\left(x% \right)+BY_{\nu}\left(x\right)}}$ `w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re((-\nu)+k+1)>0,\Re(n+\nu+\tfrac{% 3}{2})>0}}$	w = StruveH(nu, x) - BesselY(nu, x)+ ABesselJ(nu, x)+ BBesselY(nu, x)	w == StruveH[\[Nu], x] - BesselY[\[Nu], x]+ ABesselJ[\[Nu], x]+ BBesselY[\[Nu], x]	Failure	Failure	Failed [300 / 300] Result: -.4449553305+.6668360043I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 3/2} Result: .1477245032+1.196204678I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 1/2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.4449553308212987, 0.6668360040225405] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.2518593906559602, -2.1242453536287655] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E13	${\displaystyle{\displaystyle w=\mathbf{H}_{\nu}\left(z\right)+AJ_{\nu}\left(z% \right)+B{H^{(1)}_{\nu}}\left(z\right)}}$ `w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	w = StruveH(nu, z)+ ABesselJ(nu, z)+ BHankelH1(nu, z)	w == StruveH[\[Nu], z]+ ABesselJ[\[Nu], z]+ BHankelH1[\[Nu], z]	Failure	Failure	Failed [300 / 300] Result: -.4180841979+.8728935730I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: 1.928541044+.4861253769I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.4180841980733331, 0.8728935728522607] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.285405641595042, -1.3320778184897675] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E14	${\displaystyle{\displaystyle w=\mathbf{H}_{\nu}\left(z\right)+AJ_{\nu}\left(z% \right)+B{H^{(2)}_{\nu}}\left(z\right)}}$ `w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	w = StruveH(nu, z)+ ABesselJ(nu, z)+ BHankelH2(nu, z)	w == StruveH[\[Nu], z]+ ABesselJ[\[Nu], z]+ BHankelH2[\[Nu], z]	Failure	Failure	Failed [300 / 300] Result: .1098269700-.5965662020I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: .3171413600-.3710144720I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.109826969919957, -0.5965662019254474] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.9889109079558663, -0.015623729667162342] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E15	${\displaystyle{\displaystyle w=\mathbf{K}_{\nu}\left(z\right)+A{H^{(1)}_{\nu}}% \left(z\right)+B{H^{(2)}_{\nu}}\left(z\right)}}$ `w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re((-\nu)+k+1)>0,\Re(n+\nu+\tfrac{% 3}{2})>0}}$	w = StruveH(nu, z) - BesselY(nu, z)+ AHankelH1(nu, z)+ BHankelH2(nu, z)	w == StruveH[\[Nu], z] - BesselY[\[Nu], z]+ AHankelH1[\[Nu], z]+ BHankelH2[\[Nu], z]	Failure	Failure	Failed [300 / 300] Result: -.9224011534+.2769363875I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: 1.154538681+.9695969456I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.9224011534734378, 0.27693638794598185] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.3912406162671118, -1.5643629838862487] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E16	${\displaystyle{\displaystyle w=\mathbf{L}_{\nu}\left(z\right)+AK_{\nu}\left(z% \right)+BI_{\nu}\left(z\right)}}$ `w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	w = StruveL(nu, z)+ ABesselK(nu, z)+ BBesselI(nu, z)	w == StruveL[\[Nu], z]+ ABesselK[\[Nu], z]+ BBesselI[\[Nu], z]	Failure	Failure	Failed [300 / 300] Result: -.4427134717+.1412701443I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: .8499113341+3.412421345I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.4427134718200613, 0.1412701442672558] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.8647663358395983, -0.37009195882490975] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.2.E17	${\displaystyle{\displaystyle w=\mathbf{M}_{\nu}\left(z\right)+AK_{\nu}\left(z% \right)+BI_{\nu}\left(z\right)}}$ `w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}`	${\displaystyle{\displaystyle\Re(\nu+k+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	w = StruveL(nu, z) - BesselI(nu, z)+ ABesselK(nu, z)+ BBesselI(nu, z)	w == StruveL[\[Nu], z] - BesselI[\[Nu], z]+ ABesselK[\[Nu], z]+ BBesselI[\[Nu], z]	Failure	Failure	Failed [300 / 300] Result: .876284277e-1+.1517241441I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: .9234962821+3.599925727I Test Values: {A = 1/23^(1/2)+1/2I, B = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.08762842754807953, 0.15172414402816306] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.09828151494898707, -0.22324970290386212] Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/11.2.E1 11.2.E1] || [[Item:Q3916|<math>\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{(n+\tfrac{3}{2})} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = ((1)/(2)*z)^(nu + 1)* sum(((- 1)^(n)*((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == (Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(- 1)^(n)*(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.2.E1 11.2.E1] || <math qid="Q3916">\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveH{\nu}@{z} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{(n+\tfrac{3}{2})} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) = ((1)/(2)*z)^(nu + 1)* sum(((- 1)^(n)*((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] == (Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(- 1)^(n)*(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.2.E2 11.2.E2] || [[Item:Q3917|<math>\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}</syntaxhighlight> || <math>\realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) = - I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] == - I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.240284959+1.629557917*I
+| [https://dlmf.nist.gov/11.2.E2 11.2.E2] || <math qid="Q3917">\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveL{\nu}@{z} = -ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz}</syntaxhighlight> || <math>\realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) = - I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] == - I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.240284959+1.629557917*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 33.65868914+29.08337177*I
 Test Values: {nu = -1/2+1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2402849561066787, 1.6295579188731661]
@@ Line 22: / Line 22: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E2 11.2.E2] || [[Item:Q3917|<math>-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{(n+\nu+\tfrac{3}{2})} > 0, \realpart@@{(n+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>- I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z) = ((1)/(2)*z)^(nu + 1)* sum((((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z] == (Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.240284959-1.629557917*I
+| [https://dlmf.nist.gov/11.2.E2 11.2.E2] || <math qid="Q3917">-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-ie^{-\frac{1}{2}\pi i\nu}\StruveH{\nu}@{iz} = (\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n}}{\EulerGamma@{n+\tfrac{3}{2}}\EulerGamma@{n+\nu+\tfrac{3}{2}}}</syntaxhighlight> || <math>\realpart@@{(n+\nu+\tfrac{3}{2})} > 0, \realpart@@{(n+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>- I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z) = ((1)/(2)*z)^(nu + 1)* sum((((1)/(2)*z)^(2*n))/(GAMMA(n +(3)/(2))*GAMMA(n + nu +(3)/(2))), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z] == (Divide[1,2]*z)^(\[Nu]+ 1)* Sum[Divide[(Divide[1,2]*z)^(2*n),Gamma[n +Divide[3,2]]*Gamma[n + \[Nu]+Divide[3,2]]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.240284959-1.629557917*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -33.65868914-29.08337177*I
 Test Values: {nu = -1/2+1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2402849561066787, -1.6295579188731661]
@@ Line 28: / Line 28: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E5 11.2.E5] || [[Item:Q3920|<math>\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) - BesselY(nu, z) = StruveH(nu, z)- BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] - BesselY[\[Nu], z] == StruveH[\[Nu], z]- BesselY[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.2.E5 11.2.E5] || <math qid="Q3920">\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\StruveK{\nu}@{z} = \StruveH{\nu}@{z}-\BesselY{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveH(nu, z) - BesselY(nu, z) = StruveH(nu, z)- BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveH[\[Nu], z] - BesselY[\[Nu], z] == StruveH[\[Nu], z]- BesselY[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.2.E6 11.2.E6] || [[Item:Q3921|<math>\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) - BesselI(nu, z) = StruveL(nu, z)- BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] - BesselI[\[Nu], z] == StruveL[\[Nu], z]- BesselI[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
+| [https://dlmf.nist.gov/11.2.E6 11.2.E6] || <math qid="Q3921">\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modStruveM{\nu}@{z} = \modStruveL{\nu}@{z}-\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>StruveL(nu, z) - BesselI(nu, z) = StruveL(nu, z)- BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>StruveL[\[Nu], z] - BesselI[\[Nu], z] == StruveL[\[Nu], z]- BesselI[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/11.2.E7 11.2.E7] || [[Item:Q3922|<math>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{(\nu+\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)+(1 -((nu)^(2))/((z)^(2)))*w = (((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]+(1 -Divide[\[Nu]^(2),(z)^(2)])*w == Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5630887369+.2307852889*I
+| [https://dlmf.nist.gov/11.2.E7 11.2.E7] || <math qid="Q3922">\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{(\nu+\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)+(1 -((nu)^(2))/((z)^(2)))*w = (((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]+(1 -Divide[\[Nu]^(2),(z)^(2)])*w == Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5630887369+.2307852889*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.502962248+1.156533180*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.563088736999922, 0.23078528896155245]
@@ Line 38: / Line 38: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E8 11.2.E8] || [[Item:Q3923|<math>w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(n+\nu+\tfrac{3}{2})} > 0, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z); StruveH(nu, z) - BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]
+| [https://dlmf.nist.gov/11.2.E8 11.2.E8] || <math qid="Q3923">w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z},\StruveK{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(n+\nu+\tfrac{3}{2})} > 0, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z); StruveH(nu, z) - BesselY(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]
   StruveH[\[Nu], z] - BesselY[\[Nu], z]</syntaxhighlight> || Failure || Failure || Error || Error
 |-
-| [https://dlmf.nist.gov/11.2.E9 11.2.E9] || [[Item:Q3924|<math>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{(\nu+\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)-(1 +((nu)^(2))/((z)^(2)))*w = (((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]-(1 +Divide[\[Nu]^(2),(z)^(2)])*w == Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.295139545-.7692147111*I
+| [https://dlmf.nist.gov/11.2.E9 11.2.E9] || <math qid="Q3924">\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\frac{1}{z}\deriv{w}{z}-\left(1+\frac{\nu^{2}}{z^{2}}\right)w = \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{(\nu+\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1)/(z)*diff(w, z)-(1 +((nu)^(2))/((z)^(2)))*w = (((1)/(2)*z)^(nu - 1))/(sqrt(Pi)*GAMMA(nu +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+Divide[1,z]*D[w, z]-(1 +Divide[\[Nu]^(2),(z)^(2)])*w == Divide[(Divide[1,2]*z)^(\[Nu]- 1),Sqrt[Pi]*Gamma[\[Nu]+Divide[1,2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.295139545-.7692147111*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2290885595+.1565331804*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.2951395445687996, -0.7692147110384474]
@@ Line 47: / Line 47: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E10 11.2.E10] || [[Item:Q3925|<math>w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z); StruveL(nu, z) - BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z]
+| [https://dlmf.nist.gov/11.2.E10 11.2.E10] || <math qid="Q3925">w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveL{\nu}@{z},\modStruveM{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z); StruveL(nu, z) - BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z]
   StruveL[\[Nu], z] - BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || Error || Error
 |-
-| [https://dlmf.nist.gov/11.2.E11 11.2.E11] || [[Item:Q3926|<math>w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.568729179e-1+1.004857129*I
+| [https://dlmf.nist.gov/11.2.E11 11.2.E11] || <math qid="Q3926">w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.568729179e-1+1.004857129*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.306236381+1.613216681*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.056872918319905263, 1.0048571288175818]
@@ Line 56: / Line 56: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E12 11.2.E12] || [[Item:Q3927|<math>w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, x) - BesselY(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], x] - BesselY[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4449553305+.6668360043*I
+| [https://dlmf.nist.gov/11.2.E12 11.2.E12] || <math qid="Q3927">w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveK{\nu}@{x}+A\BesselJ{\nu}@{x}+B\BesselY{\nu}@{x}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, x) - BesselY(nu, x)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], x] - BesselY[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4449553305+.6668360043*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1477245032+1.196204678*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4449553308212987, 0.6668360040225405]
@@ Line 62: / Line 62: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E13 11.2.E13] || [[Item:Q3928|<math>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH1(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH1[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4180841979+.8728935730*I
+| [https://dlmf.nist.gov/11.2.E13 11.2.E13] || <math qid="Q3928">w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{1}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH1(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH1[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4180841979+.8728935730*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.928541044+.4861253769*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4180841980733331, 0.8728935728522607]
@@ Line 68: / Line 68: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E14 11.2.E14] || [[Item:Q3929|<math>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1098269700-.5965662020*I
+| [https://dlmf.nist.gov/11.2.E14 11.2.E14] || <math qid="Q3929">w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveH{\nu}@{z}+A\BesselJ{\nu}@{z}+B\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z)+ A*BesselJ(nu, z)+ B*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1098269700-.5965662020*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3171413600-.3710144720*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.109826969919957, -0.5965662019254474]
@@ Line 74: / Line 74: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E15 11.2.E15] || [[Item:Q3930|<math>w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z) - BesselY(nu, z)+ A*HankelH1(nu, z)+ B*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z] - BesselY[\[Nu], z]+ A*HankelH1[\[Nu], z]+ B*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9224011534+.2769363875*I
+| [https://dlmf.nist.gov/11.2.E15 11.2.E15] || <math qid="Q3930">w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \StruveK{\nu}@{z}+A\HankelH{1}{\nu}@{z}+B\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveH(nu, z) - BesselY(nu, z)+ A*HankelH1(nu, z)+ B*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveH[\[Nu], z] - BesselY[\[Nu], z]+ A*HankelH1[\[Nu], z]+ B*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9224011534+.2769363875*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.154538681+.9695969456*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.9224011534734378, 0.27693638794598185]
@@ Line 80: / Line 80: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E16 11.2.E16] || [[Item:Q3931|<math>w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4427134717+.1412701443*I
+| [https://dlmf.nist.gov/11.2.E16 11.2.E16] || <math qid="Q3931">w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveL{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4427134717+.1412701443*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8499113341+3.412421345*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.4427134718200613, 0.1412701442672558]
@@ Line 86: / Line 86: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/11.2.E17 11.2.E17] || [[Item:Q3932|<math>w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z) - BesselI(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z] - BesselI[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .876284277e-1+.1517241441*I
+| [https://dlmf.nist.gov/11.2.E17 11.2.E17] || <math qid="Q3932">w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \modStruveM{\nu}@{z}+A\modBesselK{\nu}@{z}+B\modBesselI{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{(n+\nu+\tfrac{3}{2})} > 0</math> || <syntaxhighlight lang=mathematica>w = StruveL(nu, z) - BesselI(nu, z)+ A*BesselK(nu, z)+ B*BesselI(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == StruveL[\[Nu], z] - BesselI[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .876284277e-1+.1517241441*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9234962821+3.599925727*I
 Test Values: {A = 1/2*3^(1/2)+1/2*I, B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.08762842754807953, 0.15172414402816306]

11.2: Difference between revisions

Latest revision as of 11:28, 28 June 2021

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