11.2

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)^(2*n))/(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)^(2*n),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) = - I*exp(-(1)/(2)*Pi*I*nu)*StruveH(nu, I*z)	StruveL[\[Nu], z] == - I*Exp[-Divide[1,2]*Pi*I*\[Nu]]*StruveH[\[Nu], I*z]	Failure	Failure	Failed [8 / 70] 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)} 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)} ... 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}}}	${\displaystyle{\displaystyle\Re(n+\nu+\tfrac{3}{2})>0,\Re(n+\tfrac{3}{2})>0}}$	- 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)	- 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]	Failure	Failure	Failed [8 / 70] 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)} 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)} ... 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+.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} 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)} ... 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-.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} 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)} ... 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)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)	w == StruveH[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]	Failure	Failure	Failed [300 / 300] 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} 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} ... 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)+ A*BesselJ(nu, x)+ B*BesselY(nu, x)	w == StruveH[\[Nu], x] - BesselY[\[Nu], x]+ A*BesselJ[\[Nu], x]+ B*BesselY[\[Nu], x]	Failure	Failure	Failed [300 / 300] 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} 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} ... 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)+ A*BesselJ(nu, z)+ B*HankelH1(nu, z)	w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH1[\[Nu], z]	Failure	Failure	Failed [300 / 300] 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} 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)} ... 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)+ A*BesselJ(nu, z)+ B*HankelH2(nu, z)	w == StruveH[\[Nu], z]+ A*BesselJ[\[Nu], z]+ B*HankelH2[\[Nu], z]	Failure	Failure	Failed [300 / 300] 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} 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)} ... 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)+ A*HankelH1(nu, z)+ B*HankelH2(nu, z)	w == StruveH[\[Nu], z] - BesselY[\[Nu], z]+ A*HankelH1[\[Nu], z]+ B*HankelH2[\[Nu], z]	Failure	Failure	Failed [300 / 300] 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} 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)} ... 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)+ A*BesselK(nu, z)+ B*BesselI(nu, z)	w == StruveL[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]	Failure	Failure	Failed [300 / 300] 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} 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)} ... 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)+ A*BesselK(nu, z)+ B*BesselI(nu, z)	w == StruveL[\[Nu], z] - BesselI[\[Nu], z]+ A*BesselK[\[Nu], z]+ B*BesselI[\[Nu], z]	Failure	Failure	Failed [300 / 300] 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} 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)} ... 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