10.32: Difference between revisions

Latest revision as of 11:25, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.32.E1	${\displaystyle{\displaystyle I_{0}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^% {+z\cos\theta}\mathrm{d}\theta}}$ `\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}`	${\displaystyle{\displaystyle\Re(0+k+1)>0}}$	BesselI(0, z) = (1)/(Pi)int(exp(+ zcos(theta)), theta = 0..Pi)	BesselI[0, z] == Divide[1,Pi]Integrate[Exp[+ zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.32.E1	${\displaystyle{\displaystyle I_{0}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^% {-z\cos\theta}\mathrm{d}\theta}}$ `\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}`	${\displaystyle{\displaystyle\Re(0+k+1)>0}}$	BesselI(0, z) = (1)/(Pi)int(exp(- zcos(theta)), theta = 0..Pi)	BesselI[0, z] == Divide[1,Pi]Integrate[Exp[- zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.32.E1	${\displaystyle{\displaystyle\frac{1}{\pi}\int_{0}^{\pi}e^{+z\cos\theta}\mathrm% {d}\theta=\frac{1}{\pi}\int_{0}^{\pi}\cosh\left(z\cos\theta\right)\mathrm{d}% \theta}}$ `\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}`	${\displaystyle{\displaystyle\Re(0+k+1)>0}}$	(1)/(Pi)int(exp(+ zcos(theta)), theta = 0..Pi) = (1)/(Pi)int(cosh(zcos(theta)), theta = 0..Pi)	Divide[1,Pi]Integrate[Exp[+ zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]Integrate[Cosh[zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Successful [Tested: 7]
10.32.E1	${\displaystyle{\displaystyle\frac{1}{\pi}\int_{0}^{\pi}e^{-z\cos\theta}\mathrm% {d}\theta=\frac{1}{\pi}\int_{0}^{\pi}\cosh\left(z\cos\theta\right)\mathrm{d}% \theta}}$ `\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}`	${\displaystyle{\displaystyle\Re(0+k+1)>0}}$	(1)/(Pi)int(exp(- zcos(theta)), theta = 0..Pi) = (1)/(Pi)int(cosh(zcos(theta)), theta = 0..Pi)	Divide[1,Pi]Integrate[Exp[- zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]Integrate[Cosh[zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Successful [Tested: 7]
10.32.E2	${\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}% {\pi^{\frac{1}{2}}\Gamma\left(\nu+\frac{1}{2}\right)}\int_{0}^{\pi}e^{+z\cos% \theta}(\sin\theta)^{2\nu}\mathrm{d}\theta}}$ `\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},\Re(\nu+\frac{1}{2})>0,\Re(% \nu+k+1)>0}}$	BesselI(nu, z) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(+ zcos(theta))(sin(theta))^(2nu), theta = 0..Pi)	BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[+ zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 35]
10.32.E2	${\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}% {\pi^{\frac{1}{2}}\Gamma\left(\nu+\frac{1}{2}\right)}\int_{0}^{\pi}e^{-z\cos% \theta}(\sin\theta)^{2\nu}\mathrm{d}\theta}}$ `\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},\Re(\nu+\frac{1}{2})>0,\Re(% \nu+k+1)>0}}$	BesselI(nu, z) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(- zcos(theta))(sin(theta))^(2nu), theta = 0..Pi)	BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 35]
10.32.E2	${\displaystyle{\displaystyle\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}% \Gamma\left(\nu+\frac{1}{2}\right)}\int_{0}^{\pi}e^{+z\cos\theta}(\sin\theta)^% {2\nu}\mathrm{d}\theta=\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\Gamma% \left(\nu+\frac{1}{2}\right)}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+zt}% \mathrm{d}t}}$ `\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},\Re(\nu+\frac{1}{2})>0,\Re(% \nu+k+1)>0}}$	(((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(+ zcos(theta))(sin(theta))^(2nu), theta = 0..Pi) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int((1 - (t)^(2))^(nu -(1)/(2)) exp(+ z*t), t = - 1..1)	Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[+ zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2]) Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 35]
10.32.E2	${\displaystyle{\displaystyle\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}% \Gamma\left(\nu+\frac{1}{2}\right)}\int_{0}^{\pi}e^{-z\cos\theta}(\sin\theta)^% {2\nu}\mathrm{d}\theta=\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\Gamma% \left(\nu+\frac{1}{2}\right)}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{-zt}% \mathrm{d}t}}$ `\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},\Re(\nu+\frac{1}{2})>0,\Re(% \nu+k+1)>0}}$	(((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(- zcos(theta))(sin(theta))^(2nu), theta = 0..Pi) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int((1 - (t)^(2))^(nu -(1)/(2)) exp(- z*t), t = - 1..1)	Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2]) Exp[- z*t], {t, - 1, 1}, GenerateConditions->None]	Error	Aborted	Skip - symbolical successful subtest	Successful [Tested: 35]
10.32.E3	${\displaystyle{\displaystyle I_{n}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^% {z\cos\theta}\cos\left(n\theta\right)\mathrm{d}\theta}}$ `\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}`	${\displaystyle{\displaystyle\Re(n+k+1)>0}}$	BesselI(n, z) = (1)/(Pi)int(exp(zcos(theta))cos(ntheta), theta = 0..Pi)	BesselI[n, z] == Divide[1,Pi]Integrate[Exp[zCos[\[Theta]]]Cos[n\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 21]	Skipped - Because timed out
10.32.E4	${\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}% e^{z\cos\theta}\cos\left(\nu\theta\right)\mathrm{d}\theta-\frac{\sin\left(\nu% \pi\right)}{\pi}\int_{0}^{\infty}e^{-z\cosh t-\nu t}\mathrm{d}t}}$ `\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\tfrac{1}{2}\pi,\Re(\nu+k+1)>% 0}}$	BesselI(nu, z) = (1)/(Pi)int(exp(zcos(theta))cos(nutheta), theta = 0..Pi)-(sin(nuPi))/(Pi)int(exp(- zcosh(t)- nut), t = 0..infinity)	BesselI[\[Nu], z] == Divide[1,Pi]Integrate[Exp[zCos[\[Theta]]]Cos[\[Nu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]Pi],Pi]Integrate[Exp[- zCosh[t]- \[Nu]t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E5	${\displaystyle{\displaystyle K_{0}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\pi}e% ^{+z\cos\theta}\left(\gamma+\ln\left(2z(\sin\theta)^{2}\right)\right)\mathrm{d% }\theta}}$ `\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}`		BesselK(0, z) = -(1)/(Pi)int(exp(+ zcos(theta))(gamma + ln(2z*(sin(theta))^(2))), theta = 0..Pi)	BesselK[0, z] == -Divide[1,Pi]Integrate[Exp[+ zCos[\[Theta]]](EulerGamma + Log[2z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E5	${\displaystyle{\displaystyle K_{0}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\pi}e% ^{-z\cos\theta}\left(\gamma+\ln\left(2z(\sin\theta)^{2}\right)\right)\mathrm{d% }\theta}}$ `\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}`		BesselK(0, z) = -(1)/(Pi)int(exp(- zcos(theta))(gamma + ln(2z*(sin(theta))^(2))), theta = 0..Pi)	BesselK[0, z] == -Divide[1,Pi]Integrate[Exp[- zCos[\[Theta]]](EulerGamma + Log[2z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E6	${\displaystyle{\displaystyle K_{0}\left(x\right)=\int_{0}^{\infty}\cos\left(x% \sinh t\right)\mathrm{d}t}}$ `\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}`	${\displaystyle{\displaystyle x>0}}$	BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity)	BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]	Successful	Aborted	-	Skipped - Because timed out
10.32.E6	${\displaystyle{\displaystyle\int_{0}^{\infty}\cos\left(x\sinh t\right)\mathrm{% d}t=\int_{0}^{\infty}\frac{\cos\left(xt\right)}{\sqrt{t^{2}+1}}\mathrm{d}t}}$ `\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}`	${\displaystyle{\displaystyle x>0}}$	int(cos(xsinh(t)), t = 0..infinity) = int((cos(xt))/(sqrt((t)^(2)+ 1)), t = 0..infinity)	Integrate[Cos[xSinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[xt],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None]	Successful	Aborted	-	Skipped - Because timed out
10.32.E7	${\displaystyle{\displaystyle K_{\nu}\left(x\right)=\sec\left(\tfrac{1}{2}\nu% \pi\right)\int_{0}^{\infty}\cos\left(x\sinh t\right)\cosh\left(\nu t\right)% \mathrm{d}t}}$ `\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}`	${\displaystyle{\displaystyle\|\Re\nu\|<1,x>0}}$	BesselK(nu, x) = sec((1)/(2)nuPi)int(cos(xsinh(t))cosh(nut), t = 0..infinity)	BesselK[\[Nu], x] == Sec[Divide[1,2]\[Nu]Pi]Integrate[Cos[xSinh[t]]Cosh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E7	${\displaystyle{\displaystyle\sec\left(\tfrac{1}{2}\nu\pi\right)\int_{0}^{% \infty}\cos\left(x\sinh t\right)\cosh\left(\nu t\right)\mathrm{d}t=\csc\left(% \tfrac{1}{2}\nu\pi\right)\int_{0}^{\infty}\sin\left(x\sinh t\right)\sinh\left(% \nu t\right)\mathrm{d}t}}$ `\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}`	${\displaystyle{\displaystyle\|\Re\nu\|<1,x>0}}$	sec((1)/(2)nuPi)int(cos(xsinh(t))cosh(nut), t = 0..infinity) = csc((1)/(2)nuPi)int(sin(xsinh(t))sinh(nut), t = 0..infinity)	Sec[Divide[1,2]\[Nu]Pi]Integrate[Cos[xSinh[t]]Cosh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]\[Nu]Pi]Integrate[Sin[xSinh[t]]Sinh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E8	${\displaystyle{\displaystyle K_{\nu}\left(z\right)=\frac{\pi^{\frac{1}{2}}(% \frac{1}{2}z)^{\nu}}{\Gamma\left(\nu+\frac{1}{2}\right)}\int_{0}^{\infty}e^{-z% \cosh t}(\sinh t)^{2\nu}\mathrm{d}t}}$ `\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},\|\operatorname{ph}z\|<\tfrac{1% }{2}\pi,\Re(\nu+\frac{1}{2})>0}}$	BesselK(nu, z) = ((Pi)^((1)/(2))((1)/(2)z)^(nu))/(GAMMA(nu +(1)/(2)))int(exp(- zcosh(t))(sinh(t))^(2nu), t = 0..infinity)	BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCosh[t]](Sinh[t])^(2\[Nu]), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E8	${\displaystyle{\displaystyle\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{% \Gamma\left(\nu+\frac{1}{2}\right)}\int_{0}^{\infty}e^{-z\cosh t}(\sinh t)^{2% \nu}\mathrm{d}t=\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\Gamma\left(\nu+% \frac{1}{2}\right)}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\mathrm{% d}t}}$ `\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},\|\operatorname{ph}z\|<\tfrac{1% }{2}\pi,\Re(\nu+\frac{1}{2})>0}}$	((Pi)^((1)/(2))((1)/(2)z)^(nu))/(GAMMA(nu +(1)/(2)))int(exp(- zcosh(t))(sinh(t))^(2nu), t = 0..infinity) = ((Pi)^((1)/(2))((1)/(2)z)^(nu))/(GAMMA(nu +(1)/(2)))int(exp(- zt)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1..infinity)	Divide[(Pi)^(Divide[1,2])(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCosh[t]](Sinh[t])^(2\[Nu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Pi)^(Divide[1,2])(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zt]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1, Infinity}, GenerateConditions->None]	Error	Aborted	Skip - symbolical successful subtest	Skipped - Because timed out
10.32.E9	${\displaystyle{\displaystyle K_{\nu}\left(z\right)=\int_{0}^{\infty}e^{-z\cosh t% }\cosh\left(\nu t\right)\mathrm{d}t}}$ `\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\tfrac{1}{2}\pi}}$	BesselK(nu, z) = int(exp(- zcosh(t))cosh(nu*t), t = 0..infinity)	BesselK[\[Nu], z] == Integrate[Exp[- zCosh[t]]Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E10	${\displaystyle{\displaystyle K_{\nu}\left(z\right)=\tfrac{1}{2}(\tfrac{1}{2}z)% ^{\nu}\int_{0}^{\infty}\exp\left(-t-\frac{z^{2}}{4t}\right)\frac{\mathrm{d}t}{% t^{\nu+1}}}}$ `\modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\tfrac{1}{4}\pi}}$	BesselK(nu, z) = (1)/(2)((1)/(2)z)^(nu)* int(exp(- t -((z)^(2))/(4t))(1)/((t)^(nu + 1)), t = 0..infinity)	BesselK[\[Nu], z] == Divide[1,2](Divide[1,2]z)^\[Nu]* Integrate[Exp[- t -Divide[(z)^(2),4t]]Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	-	Successful [Tested: 40]
10.32.E11	${\displaystyle{\displaystyle K_{\nu}\left(xz\right)=\frac{\Gamma\left(\nu+% \frac{1}{2}\right)(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{% \cos\left(xt\right)\mathrm{d}t}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}}}$ `\modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}`	${\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},x>0,\|\operatorname{ph}z\|<% \tfrac{1}{2}\pi,\Re(\nu+\frac{1}{2})>0}}$	BesselK(nu, x(x + yI)) = (GAMMA(nu +(1)/(2))(2(x + yI))^(nu))/((Pi)^((1)/(2)) (x)^(nu))int((cos(xt))/(((t)^(2)+(x + y*I)^(2))^(nu +(1)/(2))), t = 0..infinity)	BesselK[\[Nu], x(x + yI)] == Divide[Gamma[\[Nu]+Divide[1,2]](2(x + yI))^\[Nu],(Pi)^(Divide[1,2]) (x)^\[Nu]]Integrate[Divide[Cos[xt],((t)^(2)+(x + y*I)^(2))^(\[Nu]+Divide[1,2])], {t, 0, Infinity}, GenerateConditions->None]	Error	Aborted	-	Skipped - Because timed out
10.32.E12	${\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{% \infty-i\pi}^{\infty+i\pi}e^{z\cosh t-\nu t}\mathrm{d}t}}$ `\modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\tfrac{1}{2}\pi,\Re(\nu+k+1)>% 0}}$	BesselI(nu, z) = (1)/(2PiI)int(exp(zcosh(t)- nut), t = infinity - IPi..infinity + I*Pi)	BesselI[\[Nu], z] == Divide[1,2PiI]Integrate[Exp[zCosh[t]- \[Nu]t], {t, Infinity - IPi, Infinity + I*Pi}, GenerateConditions->None]	Error	Failure	-	Failed [50 / 50] Result: Complex[0.5303418993681409, 0.010453999760907294] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.7664848208906112, 0.1468422559210476] Test Values: {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
10.32.E13	${\displaystyle{\displaystyle K_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}% {4\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma\left(t\right)\Gamma\left(t-\nu% \right)(\tfrac{1}{2}z)^{-2t}\mathrm{d}t}}$ `\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}`	${\displaystyle{\displaystyle c>\max(\Re\nu,0)<\frac{1}{2}\pi,\|\operatorname{ph% }z\|<\frac{1}{2}\pi,\Re t>0,\Re(t-\nu)>0}}$	BesselK(nu, z) = (((1)/(2)z)^(nu))/(4PiI)int(GAMMA(t)GAMMA(t - nu)((1)/(2)z)^(- 2t), t = c - Iinfinity..c + Iinfinity)	BesselK[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],4PiI]Integrate[Gamma[t]Gamma[t - \[Nu]](Divide[1,2]z)^(- 2t), {t, c - IInfinity, c + IInfinity}, GenerateConditions->None]	Failure	Aborted	Failed [300 / 300] Result: .5663982443-.3181066824I Test Values: {c = -3/2, nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -1.434992817-2.759712160I Test Values: {c = -3/2, nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Skipped - Because timed out
10.32.E14	${\displaystyle{\displaystyle K_{\nu}\left(z\right)=\frac{1}{2\pi^{2}i}\left(% \frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos\left(\nu\pi\right)\\int_{-i% \infty}^{i\infty}\Gamma\left(t\right)\Gamma\left(\tfrac{1}{2}-t-\nu\right)% \Gamma\left(\tfrac{1}{2}-t+\nu\right)(2z)^{t}\mathrm{d}t}}$ `\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}`	${\displaystyle{\displaystyle\nu-\tfrac{1}{2}\notin\mathbb{Z}<\tfrac{3}{2}\pi,\|% \operatorname{ph}z\|<\tfrac{3}{2}\pi,\Re t>0,\Re(\tfrac{1}{2}-t-\nu)>0,\Re(% \tfrac{1}{2}-t+\nu)>0}}$	BesselK(nu, z) = (1)/(2(Pi)^(2) I)((Pi)/(2z))^((1)/(2))* exp(- z)cos(nuPi)* int(GAMMA(t)GAMMA((1)/(2)- t - nu)GAMMA((1)/(2)- t + nu)(2z)^(t), t = - Iinfinity..Iinfinity)	BesselK[\[Nu], z] == Divide[1,2(Pi)^(2) I](Divide[Pi,2z])^(Divide[1,2])* Exp[- z]Cos[\[Nu]Pi]* Integrate[Gamma[t]Gamma[Divide[1,2]- t - \[Nu]]Gamma[Divide[1,2]- t + \[Nu]](2z)^(t), {t, - IInfinity, IInfinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E15	${\displaystyle{\displaystyle I_{\mu}\left(z\right)I_{\nu}\left(z\right)=\frac{% 2}{\pi}\int_{0}^{\frac{1}{2}\pi}I_{\mu+\nu}\left(2z\cos\theta\right)\cos\left(% (\mu-\nu)\theta\right)\mathrm{d}\theta}}$ `\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}`	${\displaystyle{\displaystyle\Re\left(\mu+\nu\right)>-1,\Re((\mu)+k+1)>0,\Re(% \nu+k+1)>0,\Re((\mu+\nu)+k+1)>0}}$	BesselI(mu, z)BesselI(nu, z) = (2)/(Pi)int(BesselI(mu + nu, 2zcos(theta))cos((mu - nu)theta), theta = 0..(1)/(2)*Pi)	BesselI[\[Mu], z]BesselI[\[Nu], z] == Divide[2,Pi]Integrate[BesselI[\[Mu]+ \[Nu], 2zCos[\[Theta]]]Cos[(\[Mu]- \[Nu])\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E16	${\displaystyle{\displaystyle I_{\mu}\left(x\right)K_{\nu}\left(x\right)=\int_{% 0}^{\infty}J_{\mu+\nu}\left(2x\sinh t\right)e^{(-\mu+\nu)t}\mathrm{d}t}}$ `\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}`	${\displaystyle{\displaystyle\Re\left(\mu-\nu\right)>-\tfrac{1}{2},\Re\left(\mu% +\nu\right)>-\tfrac{1}{2},\Re\left(\mu+\nu\right)>-1,\Re\left(\mu-\nu\right)>-% 1,x>0,\Re((\mu+\nu)+k+1)>0,\Re((\mu)+k+1)>0}}$	BesselI(mu, x)BesselK(nu, x) = int(BesselJ(mu + nu, 2xsinh(t))exp((- mu + nu)*t), t = 0..infinity)	BesselI[\[Mu], x]BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]+ \[Nu], 2xSinh[t]]Exp[(- \[Mu]+ \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]	Error	Aborted	-	Skipped - Because timed out
10.32.E16	${\displaystyle{\displaystyle I_{\mu}\left(x\right)K_{\nu}\left(x\right)=\int_{% 0}^{\infty}J_{\mu-\nu}\left(2x\sinh t\right)e^{(-\mu-\nu)t}\mathrm{d}t}}$ `\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}`	${\displaystyle{\displaystyle\Re\left(\mu-\nu\right)>-\tfrac{1}{2},\Re\left(\mu% +\nu\right)>-\tfrac{1}{2},\Re\left(\mu+\nu\right)>-1,\Re\left(\mu-\nu\right)>-% 1,x>0,\Re((\mu+\nu)+k+1)>0,\Re((\mu)+k+1)>0,\Re((\mu-\nu)+k+1)>0}}$	BesselI(mu, x)BesselK(nu, x) = int(BesselJ(mu - nu, 2xsinh(t))exp((- mu - nu)*t), t = 0..infinity)	BesselI[\[Mu], x]BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]- \[Nu], 2xSinh[t]]Exp[(- \[Mu]- \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]	Error	Aborted	-	Skipped - Because timed out
10.32.E17	${\displaystyle{\displaystyle K_{\mu}\left(z\right)K_{\nu}\left(z\right)=2\int_% {0}^{\infty}K_{\mu+\nu}\left(2z\cosh t\right)\cosh\left((\mu-\nu)t\right)% \mathrm{d}t}}$ `\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\tfrac{1}{2}\pi}}$	BesselK(mu, z)BesselK(nu, z) = 2int(BesselK(mu + nu, 2zcosh(t))cosh((mu - nu)t), t = 0..infinity)	BesselK[\[Mu], z]BesselK[\[Nu], z] == 2Integrate[BesselK[\[Mu]+ \[Nu], 2zCosh[t]]Cosh[(\[Mu]- \[Nu])t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E17	${\displaystyle{\displaystyle K_{\mu}\left(z\right)K_{\nu}\left(z\right)=2\int_% {0}^{\infty}K_{\mu-\nu}\left(2z\cosh t\right)\cosh\left((\mu+\nu)t\right)% \mathrm{d}t}}$ `\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\tfrac{1}{2}\pi}}$	BesselK(mu, z)BesselK(nu, z) = 2int(BesselK(mu - nu, 2zcosh(t))cosh((mu + nu)t), t = 0..infinity)	BesselK[\[Mu], z]BesselK[\[Nu], z] == 2Integrate[BesselK[\[Mu]- \[Nu], 2zCosh[t]]Cosh[(\[Mu]+ \[Nu])t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E18	${\displaystyle{\displaystyle K_{\nu}\left(z\right)K_{\nu}\left(\zeta\right)=% \frac{1}{2}\int_{0}^{\infty}\exp\left(-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}% \right)K_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}{t}}}$ `\modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}`	${\displaystyle{\displaystyle\|\operatorname{ph}z\|<\pi,\|\operatorname{ph}\zeta\|<% \pi,\|\operatorname{ph}\left(z+\zeta\right)\|<\tfrac{1}{4}\pi}}$	BesselK(nu, z)BesselK(nu, zeta) = (1)/(2)int(exp(-(t)/(2)-((z)^(2)+ (zeta)^(2))/(2t))BesselK(nu, (zzeta)/(t))(1)/(t), t = 0..infinity)	BesselK[\[Nu], z]BesselK[\[Nu], \[Zeta]] == Divide[1,2]Integrate[Exp[-Divide[t,2]-Divide[(z)^(2)+ \[Zeta]^(2),2t]]BesselK[\[Nu], Divide[z\[Zeta],t]]Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]	Translation Error	Translation Error	-	-
10.32.E19	${\displaystyle{\displaystyle K_{\mu}\left(z\right)K_{\nu}\left(z\right)=\frac{% 1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\Gamma\left(t+\frac{1}{2}\mu+\frac% {1}{2}\nu\right)\Gamma\left(t+\frac{1}{2}\mu-\frac{1}{2}\nu\right)\Gamma\left(% t-\frac{1}{2}\mu+\frac{1}{2}\nu\right)\Gamma\left(t-\frac{1}{2}\mu-\frac{1}{2}% \nu\right)}{\Gamma\left(2t\right)}(\tfrac{1}{2}z)^{-2t}\mathrm{d}t}}$ `\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}`	${\displaystyle{\displaystyle c>\tfrac{1}{2}(\|\Re\mu\|+\|\Re\nu\|),\|\operatorname{% ph}z\|<\tfrac{1}{2}\pi,\Re(t+\frac{1}{2}\mu+\frac{1}{2}\nu)>0,\Re(t+\frac{1}{2}% \mu-\frac{1}{2}\nu)>0,\Re(t-\frac{1}{2}\mu+\frac{1}{2}\nu)>0,\Re(t-\frac{1}{2}% \mu-\frac{1}{2}\nu)>0,\Re(2t)>0}}$	BesselK(mu, z)BesselK(nu, z) = (1)/(8PiI)int((GAMMA(t +(1)/(2)mu +(1)/(2)nu)GAMMA(t +(1)/(2)mu -(1)/(2)nu)GAMMA(t -(1)/(2)mu +(1)/(2)nu)GAMMA(t -(1)/(2)mu -(1)/(2)nu))/(GAMMA(2t))((1)/(2)z)^(- 2t), t = c - Iinfinity..c + I*infinity)	BesselK[\[Mu], z]BesselK[\[Nu], z] == Divide[1,8PiI]Integrate[Divide[Gamma[t +Divide[1,2]\[Mu]+Divide[1,2]\[Nu]]Gamma[t +Divide[1,2]\[Mu]-Divide[1,2]\[Nu]]Gamma[t -Divide[1,2]\[Mu]+Divide[1,2]\[Nu]]Gamma[t -Divide[1,2]\[Mu]-Divide[1,2]\[Nu]],Gamma[2t]](Divide[1,2]z)^(- 2t), {t, c - IInfinity, c + I*Infinity}, GenerateConditions->None]	Error	Aborted	-	Skip - No test values generated

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || [[Item:Q3521|<math>\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(0, z) = (1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || <math qid="Q3521">\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(0, z) = (1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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-| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || [[Item:Q3521|<math>\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(0, z) = (1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || <math qid="Q3521">\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(0, z) = (1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
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-| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || [[Item:Q3521|<math>\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || <math qid="Q3521">\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(exp(+ z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Successful [Tested: 7]
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-| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || [[Item:Q3521|<math>\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.32.E1 10.32.E1] || <math qid="Q3521">\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(0+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Successful [Tested: 7]
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-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || <math qid="Q3522">\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
 |-
-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || <math qid="Q3522">\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
 |-
-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(+ z*t), t = - 1..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || <math qid="Q3522">\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(+ z*t), t = - 1..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
 |-
-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(- z*t), t = - 1..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[- z*t], {t, - 1, 1}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || Skip - symbolical successful subtest || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || <math qid="Q3522">\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, \realpart@@{(\nu+\frac{1}{2})} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(- z*t), t = - 1..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[- z*t], {t, - 1, 1}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || Skip - symbolical successful subtest || Successful [Tested: 35]
 |-
-| [https://dlmf.nist.gov/10.32.E3 10.32.E3] || [[Item:Q3523|<math>\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(n, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(n*theta), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[n, z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E3 10.32.E3] || <math qid="Q3523">\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(n, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(n*theta), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[n, z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E4 10.32.E4] || [[Item:Q3524|<math>\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[\[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Cosh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E4 10.32.E4] || <math qid="Q3524">\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[\[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Cosh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E5 10.32.E5] || [[Item:Q3525|<math>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselK(0, z) = -(1)/(Pi)*int(exp(+ z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E5 10.32.E5] || <math qid="Q3525">\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselK(0, z) = -(1)/(Pi)*int(exp(+ z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E5 10.32.E5] || [[Item:Q3525|<math>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselK(0, z) = -(1)/(Pi)*int(exp(- z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E5 10.32.E5] || <math qid="Q3525">\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselK(0, z) = -(1)/(Pi)*int(exp(- z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || [[Item:Q3526|<math>\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || <math qid="Q3526">\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || [[Item:Q3526|<math>\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>int(cos(x*sinh(t)), t = 0..infinity) = int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[x*t],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || <math qid="Q3526">\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>int(cos(x*sinh(t)), t = 0..infinity) = int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[x*t],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || [[Item:Q3527|<math>\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}</syntaxhighlight> || <math>|\realpart@@{\nu}| < 1, x > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, x) = sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], x] == Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Manual Skip! || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || <math qid="Q3527">\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}</syntaxhighlight> || <math>|\realpart@@{\nu}| < 1, x > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, x) = sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], x] == Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || [[Item:Q3527|<math>\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}</syntaxhighlight> || <math>|\realpart@@{\nu}| < 1, x > 0</math> || <syntaxhighlight lang=mathematica>sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) = csc((1)/(2)*nu*Pi)*int(sin(x*sinh(t))*sinh(nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]*\[Nu]*Pi]*Integrate[Sin[x*Sinh[t]]*Sinh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || <math qid="Q3527">\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}</syntaxhighlight> || <math>|\realpart@@{\nu}| < 1, x > 0</math> || <syntaxhighlight lang=mathematica>sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) = csc((1)/(2)*nu*Pi)*int(sin(x*sinh(t))*sinh(nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]*\[Nu]*Pi]*Integrate[Sin[x*Sinh[t]]*Sinh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || [[Item:Q3528|<math>\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+\frac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || <math qid="Q3528">\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+\frac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || [[Item:Q3528|<math>\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+\frac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || <math qid="Q3528">\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+\frac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E9 10.32.E9] || [[Item:Q3529|<math>\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = int(exp(- z*cosh(t))*cosh(nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Integrate[Exp[- z*Cosh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E9 10.32.E9] || <math qid="Q3529">\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = int(exp(- z*cosh(t))*cosh(nu*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Integrate[Exp[- z*Cosh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E10 10.32.E10] || [[Item:Q3530|<math>\modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{4}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (1)/(2)*((1)/(2)*z)^(nu)* int(exp(- t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[1,2]*(Divide[1,2]*z)^\[Nu]* Integrate[Exp[- t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 40]
+| [https://dlmf.nist.gov/10.32.E10 10.32.E10] || <math qid="Q3530">\modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{4}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (1)/(2)*((1)/(2)*z)^(nu)* int(exp(- t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[1,2]*(Divide[1,2]*z)^\[Nu]* Integrate[Exp[- t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 40]
 |-
-| [https://dlmf.nist.gov/10.32.E11 10.32.E11] || [[Item:Q3531|<math>\modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, x > 0, |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+\frac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, x*(x + y*I)) = (GAMMA(nu +(1)/(2))*(2*(x + y*I))^(nu))/((Pi)^((1)/(2))* (x)^(nu))*int((cos(x*t))/(((t)^(2)+(x + y*I)^(2))^(nu +(1)/(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], x*(x + y*I)] == Divide[Gamma[\[Nu]+Divide[1,2]]*(2*(x + y*I))^\[Nu],(Pi)^(Divide[1,2])* (x)^\[Nu]]*Integrate[Divide[Cos[x*t],((t)^(2)+(x + y*I)^(2))^(\[Nu]+Divide[1,2])], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E11 10.32.E11] || <math qid="Q3531">\modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}</syntaxhighlight> || <math>\realpart@@{\nu} > -\tfrac{1}{2}, x > 0, |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+\frac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, x*(x + y*I)) = (GAMMA(nu +(1)/(2))*(2*(x + y*I))^(nu))/((Pi)^((1)/(2))* (x)^(nu))*int((cos(x*t))/(((t)^(2)+(x + y*I)^(2))^(nu +(1)/(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], x*(x + y*I)] == Divide[Gamma[\[Nu]+Divide[1,2]]*(2*(x + y*I))^\[Nu],(Pi)^(Divide[1,2])* (x)^\[Nu]]*Integrate[Divide[Cos[x*t],((t)^(2)+(x + y*I)^(2))^(\[Nu]+Divide[1,2])], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E12 10.32.E12] || [[Item:Q3532|<math>\modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (1)/(2*Pi*I)*int(exp(z*cosh(t)- nu*t), t = infinity - I*Pi..infinity + I*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Cosh[t]- \[Nu]*t], {t, Infinity - I*Pi, Infinity + I*Pi}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [50 / 50]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5303418993681409, 0.010453999760907294]
+| [https://dlmf.nist.gov/10.32.E12 10.32.E12] || <math qid="Q3532">\modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (1)/(2*Pi*I)*int(exp(z*cosh(t)- nu*t), t = infinity - I*Pi..infinity + I*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Cosh[t]- \[Nu]*t], {t, Infinity - I*Pi, Infinity + I*Pi}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [50 / 50]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5303418993681409, 0.010453999760907294]
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.7664848208906112, 0.1468422559210476]
 Test Values: {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/10.32.E13 10.32.E13] || [[Item:Q3533|<math>\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}</syntaxhighlight> || <math>c > \max(\realpart@@{\nu}, 0) < \frac{1}{2}\pi, |\phase@@{z}| < \frac{1}{2}\pi, \realpart@@{t} > 0, \realpart@@{(t-\nu)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (((1)/(2)*z)^(nu))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],4*Pi*I]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5663982443-.3181066824*I
+| [https://dlmf.nist.gov/10.32.E13 10.32.E13] || <math qid="Q3533">\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}</syntaxhighlight> || <math>c > \max(\realpart@@{\nu}, 0) < \frac{1}{2}\pi, |\phase@@{z}| < \frac{1}{2}\pi, \realpart@@{t} > 0, \realpart@@{(t-\nu)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (((1)/(2)*z)^(nu))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],4*Pi*I]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5663982443-.3181066824*I
 Test Values: {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.434992817-2.759712160*I
 Test Values: {c = -3/2, nu = 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> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E14 10.32.E14] || [[Item:Q3534|<math>\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}</syntaxhighlight> || <math>\nu-\tfrac{1}{2}\notin\Integers < \tfrac{3}{2}\pi, |\phase@@{z}| < \tfrac{3}{2}\pi, \realpart@@{t} > 0, \realpart@@{(\tfrac{1}{2}-t-\nu)} > 0, \realpart@@{(\tfrac{1}{2}-t+\nu)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (1)/(2*(Pi)^(2)* I)*((Pi)/(2*z))^((1)/(2))* exp(- z)*cos(nu*Pi)* int(GAMMA(t)*GAMMA((1)/(2)- t - nu)*GAMMA((1)/(2)- t + nu)*(2*z)^(t), t = - I*infinity..I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[1,2*(Pi)^(2)* I]*(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*Cos[\[Nu]*Pi]* Integrate[Gamma[t]*Gamma[Divide[1,2]- t - \[Nu]]*Gamma[Divide[1,2]- t + \[Nu]]*(2*z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E14 10.32.E14] || <math qid="Q3534">\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}</syntaxhighlight> || <math>\nu-\tfrac{1}{2}\notin\Integers < \tfrac{3}{2}\pi, |\phase@@{z}| < \tfrac{3}{2}\pi, \realpart@@{t} > 0, \realpart@@{(\tfrac{1}{2}-t-\nu)} > 0, \realpart@@{(\tfrac{1}{2}-t+\nu)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (1)/(2*(Pi)^(2)* I)*((Pi)/(2*z))^((1)/(2))* exp(- z)*cos(nu*Pi)* int(GAMMA(t)*GAMMA((1)/(2)- t - nu)*GAMMA((1)/(2)- t + nu)*(2*z)^(t), t = - I*infinity..I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[1,2*(Pi)^(2)* I]*(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*Cos[\[Nu]*Pi]* Integrate[Gamma[t]*Gamma[Divide[1,2]- t - \[Nu]]*Gamma[Divide[1,2]- t + \[Nu]]*(2*z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E15 10.32.E15] || [[Item:Q3535|<math>\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</syntaxhighlight> || <math>\realpart@{\mu+\nu} > -1, \realpart@@{((\mu)+k+1)} > 0, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((\mu+\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(mu, z)*BesselI(nu, z) = (2)/(Pi)*int(BesselI(mu + nu, 2*z*cos(theta))*cos((mu - nu)*theta), theta = 0..(1)/(2)*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Mu], z]*BesselI[\[Nu], z] == Divide[2,Pi]*Integrate[BesselI[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E15 10.32.E15] || <math qid="Q3535">\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</syntaxhighlight> || <math>\realpart@{\mu+\nu} > -1, \realpart@@{((\mu)+k+1)} > 0, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((\mu+\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(mu, z)*BesselI(nu, z) = (2)/(Pi)*int(BesselI(mu + nu, 2*z*cos(theta))*cos((mu - nu)*theta), theta = 0..(1)/(2)*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Mu], z]*BesselI[\[Nu], z] == Divide[2,Pi]*Integrate[BesselI[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E16 10.32.E16] || [[Item:Q3536|<math>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}</syntaxhighlight> || <math>\realpart@{\mu-\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -1, \realpart@{\mu-\nu} > -1, x > 0, \realpart@@{((\mu+\nu)+k+1)} > 0, \realpart@@{((\mu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(mu, x)*BesselK(nu, x) = int(BesselJ(mu + nu, 2*x*sinh(t))*exp((- mu + nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]+ \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]+ \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E16 10.32.E16] || <math qid="Q3536">\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}</syntaxhighlight> || <math>\realpart@{\mu-\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -1, \realpart@{\mu-\nu} > -1, x > 0, \realpart@@{((\mu+\nu)+k+1)} > 0, \realpart@@{((\mu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(mu, x)*BesselK(nu, x) = int(BesselJ(mu + nu, 2*x*sinh(t))*exp((- mu + nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]+ \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]+ \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E16 10.32.E16] || [[Item:Q3536|<math>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}</syntaxhighlight> || <math>\realpart@{\mu-\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -1, \realpart@{\mu-\nu} > -1, x > 0, \realpart@@{((\mu+\nu)+k+1)} > 0, \realpart@@{((\mu)+k+1)} > 0, \realpart@@{((\mu-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(mu, x)*BesselK(nu, x) = int(BesselJ(mu - nu, 2*x*sinh(t))*exp((- mu - nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]- \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]- \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E16 10.32.E16] || <math qid="Q3536">\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}</syntaxhighlight> || <math>\realpart@{\mu-\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -\tfrac{1}{2}, \realpart@{\mu+\nu} > -1, \realpart@{\mu-\nu} > -1, x > 0, \realpart@@{((\mu+\nu)+k+1)} > 0, \realpart@@{((\mu)+k+1)} > 0, \realpart@@{((\mu-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(mu, x)*BesselK(nu, x) = int(BesselJ(mu - nu, 2*x*sinh(t))*exp((- mu - nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]- \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]- \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || [[Item:Q3537|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]- \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || <math qid="Q3537">\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]- \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || [[Item:Q3537|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]+ \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || <math qid="Q3537">\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]+ \[Nu])*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E18 10.32.E18] || [[Item:Q3538|<math>\modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}</syntaxhighlight> || <math>|\phase@@{z}| < \pi, |\phase@@{\zeta}| < \pi, |\phase@{z+\zeta}| < \tfrac{1}{4}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z)*BesselK(nu, zeta) = (1)/(2)*int(exp(-(t)/(2)-((z)^(2)+ (zeta)^(2))/(2*t))*BesselK(nu, (z*zeta)/(t))*(1)/(t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z]*BesselK[\[Nu], \[Zeta]] == Divide[1,2]*Integrate[Exp[-Divide[t,2]-Divide[(z)^(2)+ \[Zeta]^(2),2*t]]*BesselK[\[Nu], Divide[z*\[Zeta],t]]*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Translation Error || Translation Error || - || -
+| [https://dlmf.nist.gov/10.32.E18 10.32.E18] || <math qid="Q3538">\modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}</syntaxhighlight> || <math>|\phase@@{z}| < \pi, |\phase@@{\zeta}| < \pi, |\phase@{z+\zeta}| < \tfrac{1}{4}\pi</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z)*BesselK(nu, zeta) = (1)/(2)*int(exp(-(t)/(2)-((z)^(2)+ (zeta)^(2))/(2*t))*BesselK(nu, (z*zeta)/(t))*(1)/(t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z]*BesselK[\[Nu], \[Zeta]] == Divide[1,2]*Integrate[Exp[-Divide[t,2]-Divide[(z)^(2)+ \[Zeta]^(2),2*t]]*BesselK[\[Nu], Divide[z*\[Zeta],t]]*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Translation Error || Translation Error || - || -
 |-
-| [https://dlmf.nist.gov/10.32.E19 10.32.E19] || [[Item:Q3539|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}</syntaxhighlight> || <math>c > \tfrac{1}{2}(|\realpart@@{\mu}|+|\realpart@@{\nu}|), |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(t+\frac{1}{2}\mu+\frac{1}{2}\nu)} > 0, \realpart@@{(t+\frac{1}{2}\mu-\frac{1}{2}\nu)} > 0, \realpart@@{(t-\frac{1}{2}\mu+\frac{1}{2}\nu)} > 0, \realpart@@{(t-\frac{1}{2}\mu-\frac{1}{2}\nu)} > 0, \realpart@@{(2t)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(mu, z)*BesselK(nu, z) = (1)/(8*Pi*I)*int((GAMMA(t +(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t +(1)/(2)*mu -(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu -(1)/(2)*nu))/(GAMMA(2*t))*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Mu], z]*BesselK[\[Nu], z] == Divide[1,8*Pi*I]*Integrate[Divide[Gamma[t +Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t +Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]],Gamma[2*t]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skip - No test values generated
+| [https://dlmf.nist.gov/10.32.E19 10.32.E19] || <math qid="Q3539">\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}</syntaxhighlight> || <math>c > \tfrac{1}{2}(|\realpart@@{\mu}|+|\realpart@@{\nu}|), |\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(t+\frac{1}{2}\mu+\frac{1}{2}\nu)} > 0, \realpart@@{(t+\frac{1}{2}\mu-\frac{1}{2}\nu)} > 0, \realpart@@{(t-\frac{1}{2}\mu+\frac{1}{2}\nu)} > 0, \realpart@@{(t-\frac{1}{2}\mu-\frac{1}{2}\nu)} > 0, \realpart@@{(2t)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(mu, z)*BesselK(nu, z) = (1)/(8*Pi*I)*int((GAMMA(t +(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t +(1)/(2)*mu -(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu -(1)/(2)*nu))/(GAMMA(2*t))*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Mu], z]*BesselK[\[Nu], z] == Divide[1,8*Pi*I]*Integrate[Divide[Gamma[t +Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t +Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]],Gamma[2*t]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skip - No test values generated
 |}
 </div>

10.32: Difference between revisions

Latest revision as of 11:25, 28 June 2021

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