11.7

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
11.7.E1	${\displaystyle{\displaystyle\int z^{\nu}\mathbf{H}_{\nu-1}\left(z\right)\mathrm{d}z=z^{\nu}\mathbf{H}_{\nu}\left(z\right)}}$ \int z^{\nu}\StruveH{\nu-1}@{z}\diff{z} = z^{\nu}\StruveH{\nu}@{z}	${\displaystyle{\displaystyle\Re(n+(\nu-1)+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((z)^(nu)* StruveH(nu - 1, z), z) = (z)^(nu)* StruveH(nu, z)	Integrate[(z)^\[Nu]* StruveH[\[Nu]- 1, z], z, GenerateConditions->None] == (z)^\[Nu]* StruveH[\[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
11.7.E2	${\displaystyle{\displaystyle\int z^{-\nu}\mathbf{H}_{\nu+1}\left(z\right)\mathrm{d}z=-z^{-\nu}\mathbf{H}_{\nu}\left(z\right)+\frac{2^{-\nu}z}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)}}}$ \int z^{-\nu}\StruveH{\nu+1}@{z}\diff{z} = -z^{-\nu}\StruveH{\nu}@{z}+\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}	${\displaystyle{\displaystyle\Re(\nu+\tfrac{3}{2})>0,\Re(n+(\nu+1)+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((z)^(- nu)* StruveH(nu + 1, z), z) = - (z)^(- nu)* StruveH(nu, z)+((2)^(- nu)* z)/(sqrt(Pi)*GAMMA(nu +(3)/(2)))	Integrate[(z)^(- \[Nu])* StruveH[\[Nu]+ 1, z], z, GenerateConditions->None] == - (z)^(- \[Nu])* StruveH[\[Nu], z]+Divide[(2)^(- \[Nu])* z,Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]	Successful	Successful	-	Successful [Tested: 56]
11.7.E3	${\displaystyle{\displaystyle\int z^{\nu}\mathbf{L}_{\nu-1}\left(z\right)\mathrm{d}z=z^{\nu}\mathbf{L}_{\nu}\left(z\right)}}$ \int z^{\nu}\modStruveL{\nu-1}@{z}\diff{z} = z^{\nu}\modStruveL{\nu}@{z}	${\displaystyle{\displaystyle\Re(n+(\nu-1)+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((z)^(nu)* StruveL(nu - 1, z), z) = (z)^(nu)* StruveL(nu, z)	Integrate[(z)^\[Nu]* StruveL[\[Nu]- 1, z], z, GenerateConditions->None] == (z)^\[Nu]* StruveL[\[Nu], z]	Failure	Successful	Failed [4 / 70] Result: 15.74633170+6.711214442*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} Result: 1573.901952-547.1907270*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	Successful [Tested: 70]
11.7.E4	${\displaystyle{\displaystyle\int z^{-\nu}\mathbf{L}_{\nu+1}\left(z\right)\mathrm{d}z=z^{-\nu}\mathbf{L}_{\nu}\left(z\right)-\frac{2^{-\nu}z}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)}}}$ \int z^{-\nu}\modStruveL{\nu+1}@{z}\diff{z} = z^{-\nu}\modStruveL{\nu}@{z}-\frac{2^{-\nu}z}{\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}	${\displaystyle{\displaystyle\Re(\nu+\tfrac{3}{2})>0,\Re(n+(\nu+1)+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((z)^(- nu)* StruveL(nu + 1, z), z) = (z)^(- nu)* StruveL(nu, z)-((2)^(- nu)* z)/(sqrt(Pi)*GAMMA(nu +(3)/(2)))	Integrate[(z)^(- \[Nu])* StruveL[\[Nu]+ 1, z], z, GenerateConditions->None] == (z)^(- \[Nu])* StruveL[\[Nu], z]-Divide[(2)^(- \[Nu])* z,Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]	Successful	Successful	-	Successful [Tested: 56]
11.7.E5	${\displaystyle{\displaystyle f_{\nu}(z)=\int_{0}^{z}t^{\nu}\mathbf{H}_{\nu}\left(t\right)\mathrm{d}t}}$ f_{\nu}(z) = \int_{0}^{z}t^{\nu}\StruveH{\nu}@{t}\diff{t}	${\displaystyle{\displaystyle\Re(n+\nu+\tfrac{3}{2})>0}}$	f[nu](z) = int((t)^(nu)* StruveH(nu, t), t = 0..z)	Subscript[f, \[Nu]][z] == Integrate[(t)^\[Nu]* StruveH[\[Nu], t], {t, 0, z}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: .4776177026+.8322237517*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = 1/2*3^(1/2)+1/2*I} Result: -.8884077018+.4661983481*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.4776177021895665, 0.8322237514648603] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.8884077015948724, 0.4661983476804216] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.7.E6	${\displaystyle{\displaystyle f_{\nu+1}(z)=(2\nu+1)f_{\nu}(z)-z^{\nu+1}\mathbf{H}_{\nu}\left(z\right)+\frac{(\tfrac{1}{2}z^{2})^{\nu+1}}{(\nu+1)\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)}}}$ f_{\nu+1}(z) = (2\nu+1)f_{\nu}(z)-z^{\nu+1}\StruveH{\nu}@{z}+\frac{(\tfrac{1}{2}z^{2})^{\nu+1}}{(\nu+1)\sqrt{\pi}\EulerGamma@{\nu+\tfrac{3}{2}}}	${\displaystyle{\displaystyle\Re\nu>-1,\Re(\nu+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	f[nu + 1](z) = (2*nu + 1)*f[nu](z)- (z)^(nu + 1)* StruveH(nu, z)+(((1)/(2)*(z)^(2))^(nu + 1))/((nu + 1)*sqrt(Pi)*GAMMA(nu +(3)/(2)))	Subscript[f, \[Nu]+ 1][z] == (2*\[Nu]+ 1)*Subscript[f, \[Nu]][z]- (z)^(\[Nu]+ 1)* StruveH[\[Nu], z]+Divide[(Divide[1,2]*(z)^(2))^(\[Nu]+ 1),(\[Nu]+ 1)*Sqrt[Pi]*Gamma[\[Nu]+Divide[3,2]]]	Failure	Failure	Failed [300 / 300] Result: .2926898254e-1-1.890529289*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu+1] = 1/2*3^(1/2)+1/2*I} Result: -1.336756421-2.256554693*I Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu+1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.029268983232513014, -1.8905292888907776] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.3367564205519258, -2.2565546926752162] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
11.7.E7	${\displaystyle{\displaystyle\int_{0}^{\pi/2}\mathbf{H}_{\nu}\left(z\sin\theta\right)\frac{(\sin\theta)^{\nu+1}}{(\cos\theta)^{2\nu}}\mathrm{d}\theta=\frac{2^{-\nu}}{\sqrt{\pi}}\Gamma\left(\tfrac{1}{2}-\nu\right)z^{\nu-1}(1-\cos z)}}$ \int_{0}^{\pi/2}\StruveH{\nu}@{z\sin@@{\theta}}\frac{(\sin@@{\theta})^{\nu+1}}{(\cos@@{\theta})^{2\nu}}\diff{\theta} = \frac{2^{-\nu}}{\sqrt{\pi}}\EulerGamma@{\tfrac{1}{2}-\nu}z^{\nu-1}(1-\cos@@{z})	${\displaystyle{\displaystyle-\tfrac{3}{2}<\Re\nu,\Re\nu<\tfrac{1}{2},\Re(\tfrac{1}{2}-\nu)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int(StruveH(nu, z*sin(theta))*((sin(theta))^(nu + 1))/((cos(theta))^(2*nu)), theta = 0..Pi/2) = ((2)^(- nu))/(sqrt(Pi))*GAMMA((1)/(2)- nu)*(z)^(nu - 1)*(1 - cos(z))	Integrate[StruveH[\[Nu], z*Sin[\[Theta]]]*Divide[(Sin[\[Theta]])^(\[Nu]+ 1),(Cos[\[Theta]])^(2*\[Nu])], {\[Theta], 0, Pi/2}, GenerateConditions->None] == Divide[(2)^(- \[Nu]),Sqrt[Pi]]*Gamma[Divide[1,2]- \[Nu]]*(z)^(\[Nu]- 1)*(1 - Cos[z])	Successful	Aborted	-	Successful [Tested: 21]
11.7#Ex1	${\displaystyle{\displaystyle\int_{0}^{\infty}\mathbf{H}_{0}\left(t\right)\,\frac{\mathrm{d}t}{t}=\tfrac{1}{2}\pi}}$ \int_{0}^{\infty}\StruveH{0}@{t}\,\frac{\diff{t}}{t} = \tfrac{1}{2}\pi	${\displaystyle{\displaystyle\Re(n+0+\tfrac{3}{2})>0}}$	int(StruveH(0, t)*(1)/(t), t = 0..infinity) = (1)/(2)*Pi	Integrate[StruveH[0, t]*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi	Successful	Successful	-	Successful [Tested: 1]
11.7#Ex2	${\displaystyle{\displaystyle\int_{0}^{\infty}\mathbf{H}_{1}\left(t\right)\,\frac{\mathrm{d}t}{t^{2}}=\tfrac{1}{4}\pi}}$ \int_{0}^{\infty}\StruveH{1}@{t}\,\frac{\diff{t}}{t^{2}} = \tfrac{1}{4}\pi	${\displaystyle{\displaystyle\Re(n+1+\tfrac{3}{2})>0}}$	int(StruveH(1, t)*(1)/((t)^(2)), t = 0..infinity) = (1)/(4)*Pi	Integrate[StruveH[1, t]*Divide[1,(t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,4]*Pi	Successful	Successful	-	Successful [Tested: 1]
11.7.E9	${\displaystyle{\displaystyle\int_{0}^{\infty}\mathbf{H}_{\nu}\left(t\right)\mathrm{d}t=-\cot\left(\tfrac{1}{2}\pi\nu\right)}}$ \int_{0}^{\infty}\StruveH{\nu}@{t}\diff{t} = -\cot@{\tfrac{1}{2}\pi\nu}	${\displaystyle{\displaystyle-2<\Re\nu,\Re\nu<0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int(StruveH(nu, t), t = 0..infinity) = - cot((1)/(2)*Pi*nu)	Integrate[StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == - Cot[Divide[1,2]*Pi*\[Nu]]	Successful	Aborted	-	Successful [Tested: 4]
11.7.E10	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{-\nu-1}\mathbf{H}_{\nu}\left(t\right)\mathrm{d}t=\frac{\pi}{2^{\nu+1}\Gamma\left(\nu+1\right)}}}$ \int_{0}^{\infty}t^{-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\pi}{2^{\nu+1}\EulerGamma@{\nu+1}}	${\displaystyle{\displaystyle\Re\nu>-\tfrac{3}{2},\Re(\nu+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((t)^(- nu - 1)* StruveH(nu, t), t = 0..infinity) = (Pi)/((2)^(nu + 1)* GAMMA(nu + 1))	Integrate[(t)^(- \[Nu]- 1)* StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,(2)^(\[Nu]+ 1)* Gamma[\[Nu]+ 1]]	Successful	Aborted	-	Skipped - Because timed out
11.7.E11	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-\nu-1}\mathbf{H}_{\nu}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\tfrac{1}{2}\mu\right)2^{\mu-\nu-1}\tan\left(\tfrac{1}{2}\pi\mu\right)}{\Gamma\left(\nu-\tfrac{1}{2}\mu+1\right)}}}$ \int_{0}^{\infty}t^{\mu-\nu-1}\StruveH{\nu}@{t}\diff{t} = \frac{\EulerGamma@{\tfrac{1}{2}\mu}2^{\mu-\nu-1}\tan@{\tfrac{1}{2}\pi\mu}}{\EulerGamma@{\nu-\tfrac{1}{2}\mu+1}}	${\displaystyle{\displaystyle|\Re\mu|<1,\Re\nu>\Re\mu-\tfrac{3}{2},\Re(\tfrac{1}{2}\mu)>0,\Re(\nu-\tfrac{1}{2}\mu+1)>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((t)^(mu - nu - 1)* StruveH(nu, t), t = 0..infinity) = (GAMMA((1)/(2)*mu)*(2)^(mu - nu - 1)* tan((1)/(2)*Pi*mu))/(GAMMA(nu -(1)/(2)*mu + 1))	Integrate[(t)^(\[Mu]- \[Nu]- 1)* StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]*\[Mu]]*(2)^(\[Mu]- \[Nu]- 1)* Tan[Divide[1,2]*Pi*\[Mu]],Gamma[\[Nu]-Divide[1,2]*\[Mu]+ 1]]	Successful	Aborted	-	Skipped - Because timed out
11.7.E12	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{-\mu-\nu}\mathbf{H}_{\mu}\left(t\right)\mathbf{H}_{\nu}\left(t\right)\mathrm{d}t=\frac{\sqrt{\pi}\Gamma\left(\mu+\nu\right)}{2^{\mu+\nu}\Gamma\left(\mu+\nu+\tfrac{1}{2}\right)\Gamma\left(\mu+\tfrac{1}{2}\right)\Gamma\left(\nu+\tfrac{1}{2}\right)}}}$ \int_{0}^{\infty}t^{-\mu-\nu}\StruveH{\mu}@{t}\StruveH{\nu}@{t}\diff{t} = \frac{\sqrt{\pi}\EulerGamma@{\mu+\nu}}{2^{\mu+\nu}\EulerGamma@{\mu+\nu+\tfrac{1}{2}}\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}	${\displaystyle{\displaystyle\Re\left(\mu+\nu\right)>0,\Re(\mu+\nu)>0,\Re(\mu+\nu+\tfrac{1}{2})>0,\Re(\mu+\tfrac{1}{2})>0,\Re(\nu+\tfrac{1}{2})>0,\Re(n+(\mu)+\tfrac{3}{2})>0,\Re(n+\nu+\tfrac{3}{2})>0}}$	int((t)^(- mu - nu)* StruveH(mu, t)*StruveH(nu, t), t = 0..infinity) = (sqrt(Pi)*GAMMA(mu + nu))/((2)^(mu + nu)* GAMMA(mu + nu +(1)/(2))*GAMMA(mu +(1)/(2))*GAMMA(nu +(1)/(2)))	Integrate[(t)^(- \[Mu]- \[Nu])* StruveH[\[Mu], t]*StruveH[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi]*Gamma[\[Mu]+ \[Nu]],(2)^(\[Mu]+ \[Nu])* Gamma[\[Mu]+ \[Nu]+Divide[1,2]]*Gamma[\[Mu]+Divide[1,2]]*Gamma[\[Nu]+Divide[1,2]]]	Successful	Aborted	-	Skipped - Because timed out
11.7.E13	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{H}_{0}\left(t\right)\mathrm{d}t=\frac{2}{\pi\sqrt{1+a^{2}}}\ln\left(\frac{1+\sqrt{1+a^{2}}}{a}\right)}}$ \int_{0}^{\infty}e^{-at}\StruveH{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}	${\displaystyle{\displaystyle\Re(n+0+\tfrac{3}{2})>0}}$	int(exp(- a*t)*StruveH(0, t), t = 0..infinity) = (2)/(Pi*sqrt(1 + (a)^(2)))*ln((1 +sqrt(1 + (a)^(2)))/(a))	Integrate[Exp[- a*t]*StruveH[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2,Pi*Sqrt[1 + (a)^(2)]]*Log[Divide[1 +Sqrt[1 + (a)^(2)],a]]	Failure	Aborted	Failed [3 / 6] Result: 0.-1.109400392*I Test Values: {a = -3/2} Result: .7e-9-1.788854381*I Test Values: {a = -1/2} ... skip entries to safe data	Failed [3 / 6] Result: Complex[-8.326672684688674*^-17, -1.1094003924504583] Test Values: {Rule[a, -1.5]} Result: Complex[0.0, -1.7888543819998317] Test Values: {Rule[a, -0.5]} ... skip entries to safe data
11.7.E14	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{H}_{1}\left(t\right)\mathrm{d}t=\frac{2}{\pi a}-\frac{2a}{\pi\sqrt{1+a^{2}}}\ln\left(\frac{1+\sqrt{1+a^{2}}}{a}\right)}}$ \int_{0}^{\infty}e^{-at}\StruveH{1}@{t}\diff{t} = \frac{2}{\pi a}-\frac{2a}{\pi\sqrt{1+a^{2}}}\ln@{\frac{1+\sqrt{1+a^{2}}}{a}}	${\displaystyle{\displaystyle\Re(n+1+\tfrac{3}{2})>0}}$	int(exp(- a*t)*StruveH(1, t), t = 0..infinity) = (2)/(Pi*a)-(2*a)/(Pi*sqrt(1 + (a)^(2)))*ln((1 +sqrt(1 + (a)^(2)))/(a))	Integrate[Exp[- a*t]*StruveH[1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2,Pi*a]-Divide[2*a,Pi*Sqrt[1 + (a)^(2)]]*Log[Divide[1 +Sqrt[1 + (a)^(2)],a]]	Failure	Failure	Failed [3 / 6] Result: .1865480398-1.664100588*I Test Values: {a = -3/2} Result: 1.724458563-.8944271906*I Test Values: {a = -1/2} ... skip entries to safe data	Failed [3 / 6] Result: Complex[-5.551115123125783*^-17, -1.6641005886756874] Test Values: {Rule[a, -1.5]} Result: Complex[1.1102230246251565*^-16, -0.8944271909999159] Test Values: {Rule[a, -0.5]} ... skip entries to safe data
11.7.E15	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{L}_{0}\left(t\right)\mathrm{d}t=\frac{2}{\pi\sqrt{a^{2}\!-\!1}}\operatorname{arcsin}\left(\frac{1}{a}\right)}}$ \int_{0}^{\infty}e^{-at}\modStruveL{0}@{t}\diff{t} = \frac{2}{\pi\sqrt{a^{2}\!-\!1}}\asin@{\frac{1}{a}}	${\displaystyle{\displaystyle\Re(n+0+\tfrac{3}{2})>0}}$	int(exp(- a*t)*StruveL(0, t), t = 0..infinity) = (2)/(Pi*sqrt((a)^(2)- 1))*arcsin((1)/(a))	Integrate[Exp[- a*t]*StruveL[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2,Pi*Sqrt[(a)^(2)- 1]]*ArcSin[Divide[1,a]]	Failure	Successful	Failed [4 / 6] Result: .8310285000-.2578603735e-9*I Test Values: {a = -3/2} Result: -1.936205180+0.*I Test Values: {a = -1/2} ... skip entries to safe data	Successful [Tested: 6]
11.7#Ex4	${\displaystyle{\displaystyle=\frac{2a}{\pi\sqrt{a^{2}\!-\!1}}\operatorname{arctan}\left(\frac{1}{\sqrt{a^{2}\!-\!1}}\right)-\frac{2}{\pi a}}}$ = \frac{2a}{\pi\sqrt{a^{2}\!-\!1}}\atan@{\frac{1}{\sqrt{a^{2}\!-\!1}}}-\frac{2}{\pi a}		= (2*a)/(Pi*sqrt((a)^(2)- 1))*arctan((1)/(sqrt((a)^(2)- 1)))-(2)/(Pi*a)	== Divide[2*a,Pi*Sqrt[(a)^(2)- 1]]*ArcTan[Divide[1,Sqrt[(a)^(2)- 1]]]-Divide[2,Pi*a]	Error	Failure	-	Error