Results of Confluent Hypergeometric Functions II

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.14.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}+\left(-\frac{1}{4}+\frac{\kappa}{z}+\frac{\frac{1}{4}-\mu^{2}}{z^{2}}\right)W=0}}$ \deriv[2]{W}{z}+\left(-\frac{1}{4}+\frac{\kappa}{z}+\frac{\frac{1}{4}-\mu^{2}}{z^{2}}\right)W = 0		diff(W, [z$(2)])+(-(1)/(4)+(kappa)/(z)+((1)/(4)- (mu)^(2))/((z)^(2)))*W = 0	D[W, {z, 2}]+(-Divide[1,4]+Divide[\[Kappa],z]+Divide[Divide[1,4]- \[Mu]^(2),(z)^(2)])*W == 0	Failure	Failure	Failed [300 / 300] Result: -.1000000000e-9-.2499999999*I Test Values: {W = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: .9330127021-.3660254041*I Test Values: {W = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.3877787807814457*^-17, -0.25] Test Values: {Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.7320508075688772, 0.7500000000000002] Test Values: {Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.14.E2	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}M\left(\tfrac{1}{2}+\mu-\kappa,1+2\mu,z\right)}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\KummerconfhyperM@{\tfrac{1}{2}+\mu-\kappa}{1+2\mu}{z}		WhittakerM(kappa, mu, z) = exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* KummerM((1)/(2)+ mu - kappa, 1 + 2*mu, z)	WhittakerM[\[Kappa], \[Mu], z] == Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* Hypergeometric1F1[Divide[1,2]+ \[Mu]- \[Kappa], 1 + 2*\[Mu], z]	Successful	Successful	-	Failed [78 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.14.E3	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}U\left(\tfrac{1}{2}+\mu-\kappa,1+2\mu,z\right)}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\KummerconfhyperU@{\tfrac{1}{2}+\mu-\kappa}{1+2\mu}{z}		WhittakerW(kappa, mu, z) = exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* KummerU((1)/(2)+ mu - kappa, 1 + 2*mu, z)	WhittakerW[\[Kappa], \[Mu], z] == Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* HypergeometricU[Divide[1,2]+ \[Mu]- \[Kappa], 1 + 2*\[Mu], z]	Successful	Successful	-	Successful [Tested: 300]
13.14.E4	${\displaystyle{\displaystyle M\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{2}b}M_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right)}}$ \KummerconfhyperM@{a}{b}{z} = e^{\frac{1}{2}z}z^{-\frac{1}{2}b}\WhittakerconfhyperM{\frac{1}{2}b-a}{\frac{1}{2}b-\frac{1}{2}}@{z}		KummerM(a, b, z) = exp((1)/(2)*z)*(z)^(-(1)/(2)*b)* WhittakerM((1)/(2)*b - a, (1)/(2)*b -(1)/(2), z)	Hypergeometric1F1[a, b, z] == Exp[Divide[1,2]*z]*(z)^(-Divide[1,2]*b)* WhittakerM[Divide[1,2]*b - a, Divide[1,2]*b -Divide[1,2], z]	Successful	Successful	-	Failed [35 / 252] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.14.E5	${\displaystyle{\displaystyle U\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{2}b}W_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right)}}$ \KummerconfhyperU@{a}{b}{z} = e^{\frac{1}{2}z}z^{-\frac{1}{2}b}\WhittakerconfhyperW{\frac{1}{2}b-a}{\frac{1}{2}b-\frac{1}{2}}@{z}		KummerU(a, b, z) = exp((1)/(2)*z)*(z)^(-(1)/(2)*b)* WhittakerW((1)/(2)*b - a, (1)/(2)*b -(1)/(2), z)	HypergeometricU[a, b, z] == Exp[Divide[1,2]*z]*(z)^(-Divide[1,2]*b)* WhittakerW[Divide[1,2]*b - a, Divide[1,2]*b -Divide[1,2], z]	Successful	Successful	-	Successful [Tested: 252]
13.14.E6	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(1+2\mu\right)_{s}}s!}z^{s}}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{1+2\mu}{s}s!}z^{s}		WhittakerM(kappa, mu, z) = exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* sum((pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(1 + 2*mu, s)*factorial(s))*(z)^(s), s = 0..infinity)	WhittakerM[\[Kappa], \[Mu], z] == Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* Sum[Divide[Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[1 + 2*\[Mu], s]*(s)!]*(z)^(s), {s, 0, Infinity}, GenerateConditions->None]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
13.14.E6	${\displaystyle{\displaystyle e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(1+2\mu\right)_{s}}s!}z^{s}=z^{\frac{1}{2}+\mu}\sum_{n=0}^{\infty}{{}_{2}F_{1}}\left({-n,\tfrac{1}{2}+\mu-\kappa\atop 1+2\mu};2\right)\frac{\left(-\tfrac{1}{2}z\right)^{n}}{n!}}}$ e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{1+2\mu}{s}s!}z^{s} = z^{\frac{1}{2}+\mu}\sum_{n=0}^{\infty}\genhyperF{2}{1}@@{-n,\tfrac{1}{2}+\mu-\kappa}{1+2\mu}{2}\frac{\left(-\tfrac{1}{2}z\right)^{n}}{n!}		exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* sum((pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(1 + 2*mu, s)*factorial(s))*(z)^(s), s = 0..infinity) = (z)^((1)/(2)+ mu)* sum(hypergeom([- n ,(1)/(2)+ mu - kappa], [1 + 2*mu], 2)*((-(1)/(2)*z)^(n))/(factorial(n)), n = 0..infinity)	Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* Sum[Divide[Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[1 + 2*\[Mu], s]*(s)!]*(z)^(s), {s, 0, Infinity}, GenerateConditions->None] == (z)^(Divide[1,2]+ \[Mu])* Sum[HypergeometricPFQ[{- n ,Divide[1,2]+ \[Mu]- \[Kappa]}, {1 + 2*\[Mu]}, 2]*Divide[(-Divide[1,2]*z)^(n),(n)!], {n, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 70]	Failed [70 / 70] Result: Plus[Complex[0.7625032651803492, -0.1563764235133353], Times[Complex[-0.9238795325112867, -0.3826834323650898], NSum[Times[Power[Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], n], Power[Factorial[n], -1], HypergeometricPFQ[{Plus[Rational[3, 4], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-1, n]} Test Values: {Rational[3, 2]}, 2]], {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Rational[1, 4]]} Result: Plus[Complex[1.7168297866655773, 0.2697440808837949], Times[Complex[-0.9238795325112867, -0.3826834323650898], NSum[Times[Power[Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], n], Power[Factorial[n], -1], HypergeometricPFQ[{Plus[Rational[3, 4], Times[-1, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]], Times[-1, n]} Test Values: {Rational[3, 2]}, 2]], {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[μ, Rational[1, 4]]} ... skip entries to safe data
13.14.E7	${\displaystyle{\displaystyle\frac{{\left(-\frac{1}{2}n-\kappa\right)_{n+1}}}{(n+1)!}M_{\kappa,\frac{1}{2}(n+1)}\left(z\right)=e^{-\frac{1}{2}z}z^{-\frac{1}{2}n}\sum_{s=n+1}^{\infty}\frac{{\left(-\frac{1}{2}n-\kappa\right)_{s}}}{\Gamma\left(s-n\right)s!}z^{s}}}$ \frac{\Pochhammersym{-\frac{1}{2}n-\kappa}{n+1}}{(n+1)!}\WhittakerconfhyperM{\kappa}{\frac{1}{2}(n+1)}@{z} = e^{-\frac{1}{2}z}z^{-\frac{1}{2}n}\sum_{s=n+1}^{\infty}\frac{\Pochhammersym{-\frac{1}{2}n-\kappa}{s}}{\EulerGamma@{s-n}s!}z^{s}	${\displaystyle{\displaystyle\Re(2\mu+1)>0,\Re(s-n)>0}}$	(pochhammer(-(1)/(2)*n - kappa, n + 1))/(factorial(n + 1))*WhittakerM(kappa, (1)/(2)*(n + 1), z) = exp(-(1)/(2)*z)*(z)^(-(1)/(2)*n)* sum((pochhammer(-(1)/(2)*n - kappa, s))/(GAMMA(s - n)*factorial(s))*(z)^(s), s = n + 1..infinity)	Divide[Pochhammer[-Divide[1,2]*n - \[Kappa], n + 1],(n + 1)!]*WhittakerM[\[Kappa], Divide[1,2]*(n + 1), z] == Exp[-Divide[1,2]*z]*(z)^(-Divide[1,2]*n)* Sum[Divide[Pochhammer[-Divide[1,2]*n - \[Kappa], s],Gamma[s - n]*(s)!]*(z)^(s), {s, n + 1, Infinity}, GenerateConditions->None]	Failure	Successful	Skipped - Because timed out	Successful [Tested: 210]
13.14.E8	${\displaystyle{\displaystyle W_{\kappa,+\frac{1}{2}n}\left(z\right)=\frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}}{n!\Gamma\left(\frac{1}{2}-\frac{1}{2}n-\kappa\right)}\left(\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!{\left(\kappa+\frac{1}{2}-\frac{1}{2}n\right)_{k}}}z^{-k}-\sum_{k=0}^{\infty}\frac{{\left(\frac{1}{2}n+\frac{1}{2}-\kappa\right)_{k}}}{{\left(n+1\right)_{k}}k!}z^{k}\left(\ln z+\psi\left(\tfrac{1}{2}n+\tfrac{1}{2}-\kappa+k\right)-\psi\left(1+k\right)-\psi\left(n+1+k\right)\right)\right)}}$ \WhittakerconfhyperW{\kappa}{+\frac{1}{2}n}@{z} = \frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}}{n!\EulerGamma@{\frac{1}{2}-\frac{1}{2}n-\kappa}}\left(\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!\Pochhammersym{\kappa+\frac{1}{2}-\frac{1}{2}n}{k}}z^{-k}-\sum_{k=0}^{\infty}\frac{\Pochhammersym{\frac{1}{2}n+\frac{1}{2}-\kappa}{k}}{\Pochhammersym{n+1}{k}k!}z^{k}\left(\ln@@{z}+\digamma@{\tfrac{1}{2}n+\tfrac{1}{2}-\kappa+k}-\digamma@{1+k}-\digamma@{n+1+k}\right)\right)	${\displaystyle{\displaystyle\Re(\frac{1}{2}-\frac{1}{2}n-\kappa)>0}}$	WhittakerW(kappa, +(1)/(2)*n, z) = ((- 1)^(n)* exp(-(1)/(2)*z)*(z)^((1)/(2)*n +(1)/(2)))/(factorial(n)*GAMMA((1)/(2)-(1)/(2)*n - kappa))*(sum((factorial(n)*factorial(k - 1))/(factorial(n - k)*pochhammer(kappa +(1)/(2)-(1)/(2)*n, k))*(z)^(- k), k = 1..n)- sum((pochhammer((1)/(2)*n +(1)/(2)- kappa, k))/(pochhammer(n + 1, k)*factorial(k))*(z)^(k)*(ln(z)+ Psi((1)/(2)*n +(1)/(2)- kappa + k)- Psi(1 + k)- Psi(n + 1 + k)), k = 0..infinity))	WhittakerW[\[Kappa], +Divide[1,2]*n, z] == Divide[(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*n +Divide[1,2]),(n)!*Gamma[Divide[1,2]-Divide[1,2]*n - \[Kappa]]]*(Sum[Divide[(n)!*(k - 1)!,(n - k)!*Pochhammer[\[Kappa]+Divide[1,2]-Divide[1,2]*n, k]]*(z)^(- k), {k, 1, n}, GenerateConditions->None]- Sum[Divide[Pochhammer[Divide[1,2]*n +Divide[1,2]- \[Kappa], k],Pochhammer[n + 1, k]*(k)!]*(z)^(k)*(Log[z]+ PolyGamma[Divide[1,2]*n +Divide[1,2]- \[Kappa]+ k]- PolyGamma[1 + k]- PolyGamma[n + 1 + k]), {k, 0, Infinity}, GenerateConditions->None])	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.14.E8	${\displaystyle{\displaystyle W_{\kappa,-\frac{1}{2}n}\left(z\right)=\frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}}{n!\Gamma\left(\frac{1}{2}-\frac{1}{2}n-\kappa\right)}\left(\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!{\left(\kappa+\frac{1}{2}-\frac{1}{2}n\right)_{k}}}z^{-k}-\sum_{k=0}^{\infty}\frac{{\left(\frac{1}{2}n+\frac{1}{2}-\kappa\right)_{k}}}{{\left(n+1\right)_{k}}k!}z^{k}\left(\ln z+\psi\left(\tfrac{1}{2}n+\tfrac{1}{2}-\kappa+k\right)-\psi\left(1+k\right)-\psi\left(n+1+k\right)\right)\right)}}$ \WhittakerconfhyperW{\kappa}{-\frac{1}{2}n}@{z} = \frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}}{n!\EulerGamma@{\frac{1}{2}-\frac{1}{2}n-\kappa}}\left(\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!\Pochhammersym{\kappa+\frac{1}{2}-\frac{1}{2}n}{k}}z^{-k}-\sum_{k=0}^{\infty}\frac{\Pochhammersym{\frac{1}{2}n+\frac{1}{2}-\kappa}{k}}{\Pochhammersym{n+1}{k}k!}z^{k}\left(\ln@@{z}+\digamma@{\tfrac{1}{2}n+\tfrac{1}{2}-\kappa+k}-\digamma@{1+k}-\digamma@{n+1+k}\right)\right)	${\displaystyle{\displaystyle\Re(\frac{1}{2}-\frac{1}{2}n-\kappa)>0}}$	WhittakerW(kappa, -(1)/(2)*n, z) = ((- 1)^(n)* exp(-(1)/(2)*z)*(z)^((1)/(2)*n +(1)/(2)))/(factorial(n)*GAMMA((1)/(2)-(1)/(2)*n - kappa))*(sum((factorial(n)*factorial(k - 1))/(factorial(n - k)*pochhammer(kappa +(1)/(2)-(1)/(2)*n, k))*(z)^(- k), k = 1..n)- sum((pochhammer((1)/(2)*n +(1)/(2)- kappa, k))/(pochhammer(n + 1, k)*factorial(k))*(z)^(k)*(ln(z)+ Psi((1)/(2)*n +(1)/(2)- kappa + k)- Psi(1 + k)- Psi(n + 1 + k)), k = 0..infinity))	WhittakerW[\[Kappa], -Divide[1,2]*n, z] == Divide[(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*n +Divide[1,2]),(n)!*Gamma[Divide[1,2]-Divide[1,2]*n - \[Kappa]]]*(Sum[Divide[(n)!*(k - 1)!,(n - k)!*Pochhammer[\[Kappa]+Divide[1,2]-Divide[1,2]*n, k]]*(z)^(- k), {k, 1, n}, GenerateConditions->None]- Sum[Divide[Pochhammer[Divide[1,2]*n +Divide[1,2]- \[Kappa], k],Pochhammer[n + 1, k]*(k)!]*(z)^(k)*(Log[z]+ PolyGamma[Divide[1,2]*n +Divide[1,2]- \[Kappa]+ k]- PolyGamma[1 + k]- PolyGamma[n + 1 + k]), {k, 0, Infinity}, GenerateConditions->None])	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.14.E9	${\displaystyle{\displaystyle W_{\kappa,+\frac{1}{2}n}\left(z\right)=(-1)^{\kappa-\frac{1}{2}n-\frac{1}{2}}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}\sum_{k=0}^{\kappa-\frac{1}{2}n-\frac{1}{2}}\genfrac{(}{)}{0.0pt}{}{\kappa-\frac{1}{2}n-\frac{1}{2}}{k}{\left(n+1+k\right)_{\kappa-k-\frac{1}{2}n-\frac{1}{2}}}(-z)^{k}}}$ \WhittakerconfhyperW{\kappa}{+\frac{1}{2}n}@{z} = (-1)^{\kappa-\frac{1}{2}n-\frac{1}{2}}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}\sum_{k=0}^{\kappa-\frac{1}{2}n-\frac{1}{2}}\binom{\kappa-\frac{1}{2}n-\frac{1}{2}}{k}\Pochhammersym{n+1+k}{\kappa-k-\frac{1}{2}n-\frac{1}{2}}(-z)^{k}		WhittakerW(kappa, +(1)/(2)*n, z) = (- 1)^(kappa -(1)/(2)*n -(1)/(2))* exp(-(1)/(2)*z)*(z)^((1)/(2)*n +(1)/(2))* sum(binomial(kappa -(1)/(2)*n -(1)/(2),k)*pochhammer(n + 1 + k, kappa - k -(1)/(2)*n -(1)/(2))*(- z)^(k), k = 0..kappa -(1)/(2)*n -(1)/(2))	WhittakerW[\[Kappa], +Divide[1,2]*n, z] == (- 1)^(\[Kappa]-Divide[1,2]*n -Divide[1,2])* Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*n +Divide[1,2])* Sum[Binomial[\[Kappa]-Divide[1,2]*n -Divide[1,2],k]*Pochhammer[n + 1 + k, \[Kappa]- k -Divide[1,2]*n -Divide[1,2]]*(- z)^(k), {k, 0, \[Kappa]-Divide[1,2]*n -Divide[1,2]}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 7]	Failed [189 / 210] Result: Complex[0.5169913326612593, -0.09737869271758438] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.1703866965609513, -0.19101907289178782] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.14.E9	${\displaystyle{\displaystyle W_{\kappa,-\frac{1}{2}n}\left(z\right)=(-1)^{\kappa-\frac{1}{2}n-\frac{1}{2}}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}\sum_{k=0}^{\kappa-\frac{1}{2}n-\frac{1}{2}}\genfrac{(}{)}{0.0pt}{}{\kappa-\frac{1}{2}n-\frac{1}{2}}{k}{\left(n+1+k\right)_{\kappa-k-\frac{1}{2}n-\frac{1}{2}}}(-z)^{k}}}$ \WhittakerconfhyperW{\kappa}{-\frac{1}{2}n}@{z} = (-1)^{\kappa-\frac{1}{2}n-\frac{1}{2}}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}\sum_{k=0}^{\kappa-\frac{1}{2}n-\frac{1}{2}}\binom{\kappa-\frac{1}{2}n-\frac{1}{2}}{k}\Pochhammersym{n+1+k}{\kappa-k-\frac{1}{2}n-\frac{1}{2}}(-z)^{k}		WhittakerW(kappa, -(1)/(2)*n, z) = (- 1)^(kappa -(1)/(2)*n -(1)/(2))* exp(-(1)/(2)*z)*(z)^((1)/(2)*n +(1)/(2))* sum(binomial(kappa -(1)/(2)*n -(1)/(2),k)*pochhammer(n + 1 + k, kappa - k -(1)/(2)*n -(1)/(2))*(- z)^(k), k = 0..kappa -(1)/(2)*n -(1)/(2))	WhittakerW[\[Kappa], -Divide[1,2]*n, z] == (- 1)^(\[Kappa]-Divide[1,2]*n -Divide[1,2])* Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*n +Divide[1,2])* Sum[Binomial[\[Kappa]-Divide[1,2]*n -Divide[1,2],k]*Pochhammer[n + 1 + k, \[Kappa]- k -Divide[1,2]*n -Divide[1,2]]*(- z)^(k), {k, 0, \[Kappa]-Divide[1,2]*n -Divide[1,2]}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 7]	Failed [189 / 210] Result: Complex[0.5169913326612593, -0.09737869271758438] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.1703866965609513, -0.19101907289178816] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.14.E10	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{+\pi\mathrm{i}}\right)=+\mathrm{i}e^{+\mu\pi\mathrm{i}}M_{-\kappa,\mu}\left(z\right)}}$ \WhittakerconfhyperM{\kappa}{\mu}@{ze^{+\pi\iunit}} = +\iunit e^{+\mu\pi\iunit}\WhittakerconfhyperM{-\kappa}{\mu}@{z}		WhittakerM(kappa, mu, z*exp(+ Pi*I)) = + I*exp(+ mu*Pi*I)*WhittakerM(- kappa, mu, z)	WhittakerM[\[Kappa], \[Mu], z*Exp[+ Pi*I]] == + I*Exp[+ \[Mu]*Pi*I]*WhittakerM[- \[Kappa], \[Mu], z]	Failure	Failure	Failed [130 / 300] Result: -4.895892966+1.186871174*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: .4883444919-1.278994596*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [190 / 300] Result: Complex[-4.89589296422639, 1.1868711700759136] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[16.701326575973276, -3.4860202275194005] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.14.E10	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{-\pi\mathrm{i}}\right)=-\mathrm{i}e^{-\mu\pi\mathrm{i}}M_{-\kappa,\mu}\left(z\right)}}$ \WhittakerconfhyperM{\kappa}{\mu}@{ze^{-\pi\iunit}} = -\iunit e^{-\mu\pi\iunit}\WhittakerconfhyperM{-\kappa}{\mu}@{z}		WhittakerM(kappa, mu, z*exp(- Pi*I)) = - I*exp(- mu*Pi*I)*WhittakerM(- kappa, mu, z)	WhittakerM[\[Kappa], \[Mu], z*Exp[- Pi*I]] == - I*Exp[- \[Mu]*Pi*I]*WhittakerM[- \[Kappa], \[Mu], z]	Failure	Failure	Failed [198 / 300] Result: -9.930599690-2.602006174*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)} Result: 3.613026945+13.86544735*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [140 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.14.E11	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=(-1)^{m}e^{2m\mu\pi\mathrm{i}}M_{\kappa,\mu}\left(z\right)}}$ \WhittakerconfhyperM{\kappa}{\mu}@{ze^{2m\pi\iunit}} = (-1)^{m}e^{2m\mu\pi\iunit}\WhittakerconfhyperM{\kappa}{\mu}@{z}		WhittakerM(kappa, mu, z*exp(2*m*Pi*I)) = (- 1)^(m)* exp(2*m*mu*Pi*I)*WhittakerM(kappa, mu, z)	WhittakerM[\[Kappa], \[Mu], z*Exp[2*m*Pi*I]] == (- 1)^(m)* Exp[2*m*\[Mu]*Pi*I]*WhittakerM[\[Kappa], \[Mu], z]	Failure	Failure	Failed [251 / 300] Result: .5508945958+.2826830659*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1} Result: .5259254704+.2923012958*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} ... skip entries to safe data	Failed [220 / 300] Result: Complex[0.5508945961174277, 0.2826830653610755] Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.5259254730625326, 0.2923012928351815] Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.14.E12	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=\frac{(-1)^{m+1}2\pi\mathrm{i}\sin\left(2\pi\mu m\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)\Gamma\left(1+2\mu\right)\sin\left(2\pi\mu\right)}M_{\kappa,\mu}\left(z\right)+(-1)^{m}e^{-2m\mu\pi\mathrm{i}}W_{\kappa,\mu}\left(z\right)}}$ \WhittakerconfhyperW{\kappa}{\mu}@{ze^{2m\pi\iunit}} = \frac{(-1)^{m+1}2\pi\iunit\sin@{2\pi\mu m}}{\EulerGamma@{\frac{1}{2}-\mu-\kappa}\EulerGamma@{1+2\mu}\sin@{2\pi\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z}+(-1)^{m}e^{-2m\mu\pi\iunit}\WhittakerconfhyperW{\kappa}{\mu}@{z}	${\displaystyle{\displaystyle\Re(\frac{1}{2}-\mu-\kappa)>0,\Re(1+2\mu)>0}}$	WhittakerW(kappa, mu, z*exp(2*m*Pi*I)) = ((- 1)^(m + 1)* 2*Pi*I*sin(2*Pi*mu*m))/(GAMMA((1)/(2)- mu - kappa)*GAMMA(1 + 2*mu)*sin(2*Pi*mu))*WhittakerM(kappa, mu, z)+(- 1)^(m)* exp(- 2*m*mu*Pi*I)*WhittakerW(kappa, mu, z)	WhittakerW[\[Kappa], \[Mu], z*Exp[2*m*Pi*I]] == Divide[(- 1)^(m + 1)* 2*Pi*I*Sin[2*Pi*\[Mu]*m],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]*Gamma[1 + 2*\[Mu]]*Sin[2*Pi*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]+(- 1)^(m)* Exp[- 2*m*\[Mu]*Pi*I]*WhittakerW[\[Kappa], \[Mu], z]	Failure	Failure	Failed [300 / 300] Result: -18.11244228+18.74801506*I Test Values: {kappa = -1/2+1/2*I*3^(1/2), mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1} Result: 602.4607544+35.9074468*I Test Values: {kappa = -1/2+1/2*I*3^(1/2), mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-18.112442291727014, 18.74801503541069] Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[602.4607532493621, 35.9074491081993] Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.14.E13	${\displaystyle{\displaystyle(-1)^{m}W_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=-\frac{e^{2\kappa\pi\mathrm{i}}\sin\left(2m\mu\pi\right)+\sin\left((2m-2)\mu\pi\right)}{\sin\left(2\mu\pi\right)}W_{\kappa,\mu}\left(z\right)-\frac{\sin\left(2m\mu\pi\right)2\pi\mathrm{i}e^{\kappa\pi\mathrm{i}}}{\sin\left(2\mu\pi\right)\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}W_{-\kappa,\mu}\left(ze^{\pi\mathrm{i}}\right)}}$ (-1)^{m}\WhittakerconfhyperW{\kappa}{\mu}@{ze^{2m\pi\iunit}} = -\frac{e^{2\kappa\pi\iunit}\sin@{2m\mu\pi}+\sin@{(2m-2)\mu\pi}}{\sin@{2\mu\pi}}\WhittakerconfhyperW{\kappa}{\mu}@{z}-\frac{\sin@{2m\mu\pi}2\pi\iunit e^{\kappa\pi\iunit}}{\sin@{2\mu\pi}\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\WhittakerconfhyperW{-\kappa}{\mu}@{ze^{\pi\iunit}}	${\displaystyle{\displaystyle\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	(- 1)^(m)* WhittakerW(kappa, mu, z*exp(2*m*Pi*I)) = -(exp(2*kappa*Pi*I)*sin(2*m*mu*Pi)+ sin((2*m - 2)*mu*Pi))/(sin(2*mu*Pi))*WhittakerW(kappa, mu, z)-(sin(2*m*mu*Pi)*2*Pi*I*exp(kappa*Pi*I))/(sin(2*mu*Pi)*GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))*WhittakerW(- kappa, mu, z*exp(Pi*I))	(- 1)^(m)* WhittakerW[\[Kappa], \[Mu], z*Exp[2*m*Pi*I]] == -Divide[Exp[2*\[Kappa]*Pi*I]*Sin[2*m*\[Mu]*Pi]+ Sin[(2*m - 2)*\[Mu]*Pi],Sin[2*\[Mu]*Pi]]*WhittakerW[\[Kappa], \[Mu], z]-Divide[Sin[2*m*\[Mu]*Pi]*2*Pi*I*Exp[\[Kappa]*Pi*I],Sin[2*\[Mu]*Pi]*Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*WhittakerW[- \[Kappa], \[Mu], z*Exp[Pi*I]]	Failure	Failure	Failed [300 / 300] Result: -.774951075e-1+.230823188e-1*I Test Values: {kappa = -1/2+1/2*I*3^(1/2), mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1} Result: -1.823749563+12.44290473*I Test Values: {kappa = -1/2+1/2*I*3^(1/2), mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.07749510760596677, 0.023082318493995446] Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.823749593471332, 12.442904704149905] Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.14.E25	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),M_{\kappa,-\mu}\left(z\right)\right\}=-2\mu}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperM{\kappa}{-\mu}@{z}} = -2\mu		(WhittakerM(kappa, mu, z))*diff(WhittakerM(kappa, - mu, z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerM(kappa, - mu, z)) = - 2*mu	Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerM[\[Kappa], - \[Mu], z]}, z] == - 2*\[Mu]	Failure	Failure	Failed [168 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = -3/2, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = -3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [162 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, 1.5]} ... skip entries to safe data
13.14.E26	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{\kappa,\mu}\left(z\right)\right\}=-\frac{\Gamma\left(1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperW{\kappa}{\mu}@{z}} = -\frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}	${\displaystyle{\displaystyle\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0}}$	(WhittakerM(kappa, mu, z))*diff(WhittakerW(kappa, mu, z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerW(kappa, mu, z)) = -(GAMMA(1 + 2*mu))/(GAMMA((1)/(2)+ mu - kappa))	Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[\[Kappa], \[Mu], z]}, z] == -Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]	Failure	Failure	Manual Skip!	Successful [Tested: 300]
13.14.E27	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{-\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{-(\frac{1}{2}+\mu)\pi\mathrm{i}}}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} = \frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}e^{-(\frac{1}{2}+\mu)\pi\iunit}	${\displaystyle{\displaystyle\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0}}$	(WhittakerM(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(+ Pi*I)*z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(+ Pi*I)*z)) = (GAMMA(1 + 2*mu))/(GAMMA((1)/(2)+ mu + kappa))*exp(-((1)/(2)+ mu)*Pi*I)	Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]}, z] == Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*Exp[-(Divide[1,2]+ \[Mu])*Pi*I]	Failure	Failure	Manual Skip!	Failed [52 / 300] Result: Complex[4.299229486082212, -6.012569912273703] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-4.626622324464266, 5.570319989341637] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
13.14.E27	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{-\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{+(\frac{1}{2}+\mu)\pi\mathrm{i}}}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} = \frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}e^{+(\frac{1}{2}+\mu)\pi\iunit}	${\displaystyle{\displaystyle\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0}}$	(WhittakerM(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(- Pi*I)*z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(- Pi*I)*z)) = (GAMMA(1 + 2*mu))/(GAMMA((1)/(2)+ mu + kappa))*exp(+((1)/(2)+ mu)*Pi*I)	Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]}, z] == Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*Exp[+(Divide[1,2]+ \[Mu])*Pi*I]	Failure	Failure	Manual Skip!	Failed [129 / 300] Result: Complex[-4.299229486082214, 6.012569912273712] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[4.626622324464252, -5.570319989341608] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
13.14.E28	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_{\kappa,\mu}\left(z\right)\right\}=-\frac{\Gamma\left(1-2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{-\mu}@{z},\WhittakerconfhyperW{\kappa}{\mu}@{z}} = -\frac{\EulerGamma@{1-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu-\kappa}}	${\displaystyle{\displaystyle\Re(1-2\mu)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	(WhittakerM(kappa, - mu, z))*diff(WhittakerW(kappa, mu, z), z)-diff(WhittakerM(kappa, - mu, z), z)*(WhittakerW(kappa, mu, z)) = -(GAMMA(1 - 2*mu))/(GAMMA((1)/(2)- mu - kappa))	Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[\[Kappa], \[Mu], z]}, z] == -Divide[Gamma[1 - 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]	Failure	Failure	Manual Skip!	Successful [Tested: 300]
13.14.E29	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_{-\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1-2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu+\kappa\right)}e^{-(\frac{1}{2}-\mu)\pi\mathrm{i}}}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{-\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} = \frac{\EulerGamma@{1-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa}}e^{-(\frac{1}{2}-\mu)\pi\iunit}	${\displaystyle{\displaystyle\Re(1-2\mu)>0,\Re(\frac{1}{2}-\mu+\kappa)>0}}$	(WhittakerM(kappa, - mu, z))*diff(WhittakerW(- kappa, mu, exp(+ Pi*I)*z), z)-diff(WhittakerM(kappa, - mu, z), z)*(WhittakerW(- kappa, mu, exp(+ Pi*I)*z)) = (GAMMA(1 - 2*mu))/(GAMMA((1)/(2)- mu + kappa))*exp(-((1)/(2)- mu)*Pi*I)	Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]}, z] == Divide[Gamma[1 - 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]]]*Exp[-(Divide[1,2]- \[Mu])*Pi*I]	Failure	Failure	Manual Skip!	Failed [52 / 300] Result: Complex[-4.626622324464262, 5.570319989341637] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[4.299229486082212, -6.012569912273703] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data
13.14.E29	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_{-\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1-2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu+\kappa\right)}e^{+(\frac{1}{2}-\mu)\pi\mathrm{i}}}}$ \Wronskian@{\WhittakerconfhyperM{\kappa}{-\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} = \frac{\EulerGamma@{1-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa}}e^{+(\frac{1}{2}-\mu)\pi\iunit}	${\displaystyle{\displaystyle\Re(1-2\mu)>0,\Re(\frac{1}{2}-\mu+\kappa)>0}}$	(WhittakerM(kappa, - mu, z))*diff(WhittakerW(- kappa, mu, exp(- Pi*I)*z), z)-diff(WhittakerM(kappa, - mu, z), z)*(WhittakerW(- kappa, mu, exp(- Pi*I)*z)) = (GAMMA(1 - 2*mu))/(GAMMA((1)/(2)- mu + kappa))*exp(+((1)/(2)- mu)*Pi*I)	Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]}, z] == Divide[Gamma[1 - 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]]]*Exp[+(Divide[1,2]- \[Mu])*Pi*I]	Failure	Failure	Manual Skip!	Failed [129 / 300] Result: Complex[4.626622324464292, -5.570319989341681] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[-4.299229486082212, 6.012569912273712] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data
13.14.E30	${\displaystyle{\displaystyle\mathscr{W}\left\{W_{\kappa,\mu}\left(z\right),W_{-\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)\right\}=e^{-\kappa\pi\mathrm{i}}}}$ \Wronskian@{\WhittakerconfhyperW{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} = e^{-\kappa\pi\iunit}		(WhittakerW(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(+ Pi*I)*z), z)-diff(WhittakerW(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(+ Pi*I)*z)) = exp(- kappa*Pi*I)	Wronskian[{WhittakerW[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]}, z] == Exp[- \[Kappa]*Pi*I]	Failure	Failure	Manual Skip!	Failed [160 / 300] Result: Complex[4.200902390403695, 2.050381381630863] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[4.200902390403695, 2.0503813816308636] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.14.E30	${\displaystyle{\displaystyle\mathscr{W}\left\{W_{\kappa,\mu}\left(z\right),W_{-\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)\right\}=e^{+\kappa\pi\mathrm{i}}}}$ \Wronskian@{\WhittakerconfhyperW{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} = e^{+\kappa\pi\iunit}		(WhittakerW(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(- Pi*I)*z), z)-diff(WhittakerW(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(- Pi*I)*z)) = exp(+ kappa*Pi*I)	Wronskian[{WhittakerW[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]}, z] == Exp[+ \[Kappa]*Pi*I]	Failure	Failure	Manual Skip!	Failed [80 / 300] Result: Complex[-4.200902390403696, -2.050381381630864] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-4.200902390403694, -2.050381381630864] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.14.E31	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=W_{\kappa,-\mu}\left(z\right)}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \WhittakerconfhyperW{\kappa}{-\mu}@{z}		WhittakerW(kappa, mu, z) = WhittakerW(kappa, - mu, z)	WhittakerW[\[Kappa], \[Mu], z] == WhittakerW[\[Kappa], - \[Mu], z]	Successful	Successful	-	Successful [Tested: 300]
13.14.E32	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=\frac{e^{+(\kappa-\mu-\frac{1}{2})\pi\mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}W_{\kappa,\mu}\left(z\right)+\frac{e^{+\kappa\pi\mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}W_{-\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{e^{+(\kappa-\mu-\frac{1}{2})\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\WhittakerconfhyperW{\kappa}{\mu}@{z}+\frac{e^{+\kappa\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}	${\displaystyle{\displaystyle\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0,\Re(\frac{1}{2}+\mu-\kappa)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z) = (exp(+(kappa - mu -(1)/(2))*Pi*I))/(GAMMA((1)/(2)+ mu + kappa))*WhittakerW(kappa, mu, z)+(exp(+ kappa*Pi*I))/(GAMMA((1)/(2)+ mu - kappa))*WhittakerW(- kappa, mu, exp(+ Pi*I)*z)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z] == Divide[Exp[+(\[Kappa]- \[Mu]-Divide[1,2])*Pi*I],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*WhittakerW[\[Kappa], \[Mu], z]+Divide[Exp[+ \[Kappa]*Pi*I],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]	Failure	Failure	Manual Skip!	Failed [72 / 252] Result: Complex[0.5728285416311911, 0.99341853424812] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.537549923135155, 2.4049195501566403] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
13.14.E32	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=\frac{e^{-(\kappa-\mu-\frac{1}{2})\pi\mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}W_{\kappa,\mu}\left(z\right)+\frac{e^{-\kappa\pi\mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}W_{-\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{e^{-(\kappa-\mu-\frac{1}{2})\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\WhittakerconfhyperW{\kappa}{\mu}@{z}+\frac{e^{-\kappa\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}	${\displaystyle{\displaystyle\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0,\Re(\frac{1}{2}+\mu-\kappa)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z) = (exp(-(kappa - mu -(1)/(2))*Pi*I))/(GAMMA((1)/(2)+ mu + kappa))*WhittakerW(kappa, mu, z)+(exp(- kappa*Pi*I))/(GAMMA((1)/(2)+ mu - kappa))*WhittakerW(- kappa, mu, exp(- Pi*I)*z)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z] == Divide[Exp[-(\[Kappa]- \[Mu]-Divide[1,2])*Pi*I],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*WhittakerW[\[Kappa], \[Mu], z]+Divide[Exp[- \[Kappa]*Pi*I],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]	Failure	Failure	Manual Skip!	Failed [180 / 252] Result: Complex[0.6446478863068316, -8.276809691598643] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-188.39316140446167, 86.36502083726177] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} ... skip entries to safe data
13.14.E33	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(-2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}M_{\kappa,\mu}\left(z\right)+\frac{\Gamma\left(2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}M_{\kappa,-\mu}\left(z\right)}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{\EulerGamma@{-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\WhittakerconfhyperM{\kappa}{\mu}@{z}+\frac{\EulerGamma@{2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\WhittakerconfhyperM{\kappa}{-\mu}@{z}	${\displaystyle{\displaystyle\Re(-2\mu)>0,\Re(\frac{1}{2}-\mu-\kappa)>0,\Re(2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0}}$	WhittakerW(kappa, mu, z) = (GAMMA(- 2*mu))/(GAMMA((1)/(2)- mu - kappa))*WhittakerM(kappa, mu, z)+(GAMMA(2*mu))/(GAMMA((1)/(2)+ mu - kappa))*WhittakerM(kappa, - mu, z)	WhittakerW[\[Kappa], \[Mu], z] == Divide[Gamma[- 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*WhittakerM[\[Kappa], \[Mu], z]+Divide[Gamma[2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*WhittakerM[\[Kappa], - \[Mu], z]	Successful	Failure	-	Skip - No test values generated
13.15.E1	${\displaystyle{\displaystyle(\kappa-\mu-\tfrac{1}{2})M_{\kappa-1,\mu}\left(z\right)+(z-2\kappa)M_{\kappa,\mu}\left(z\right)+(\kappa+\mu+\tfrac{1}{2})M_{\kappa+1,\mu}\left(z\right)=0}}$ (\kappa-\mu-\tfrac{1}{2})\WhittakerconfhyperM{\kappa-1}{\mu}@{z}+(z-2\kappa)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa+\mu+\tfrac{1}{2})\WhittakerconfhyperM{\kappa+1}{\mu}@{z} = 0		(kappa - mu -(1)/(2))*WhittakerM(kappa - 1, mu, z)+(z - 2*kappa)*WhittakerM(kappa, mu, z)+(kappa + mu +(1)/(2))*WhittakerM(kappa + 1, mu, z) = 0	(\[Kappa]- \[Mu]-Divide[1,2])*WhittakerM[\[Kappa]- 1, \[Mu], z]+(z - 2*\[Kappa])*WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]+Divide[1,2])*WhittakerM[\[Kappa]+ 1, \[Mu], z] == 0	Successful	Successful	-	Failed [84 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E2	${\displaystyle{\displaystyle 2\mu(1+2\mu)\sqrt{z}M_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-(z+2\mu)(1+2\mu)M_{\kappa,\mu}\left(z\right)+(\kappa+\mu+\tfrac{1}{2})\sqrt{z}M_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ 2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-(z+2\mu)(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa+\mu+\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)-(z + 2*mu)*(1 + 2*mu)*WhittakerM(kappa, mu, z)+(kappa + mu +(1)/(2))*sqrt(z)*WhittakerM(kappa +(1)/(2), mu +(1)/(2), z) = 0	2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]-(z + 2*\[Mu])*(1 + 2*\[Mu])*WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]+Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Failed [81 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E3	${\displaystyle{\displaystyle(\kappa-\mu-\tfrac{1}{2})M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)+(1+2\mu)\sqrt{z}M_{\kappa,\mu}\left(z\right)-(\kappa+\mu+\tfrac{1}{2})M_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ (\kappa-\mu-\tfrac{1}{2})\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z}+(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa}{\mu}@{z}-(\kappa+\mu+\tfrac{1}{2})\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		(kappa - mu -(1)/(2))*WhittakerM(kappa -(1)/(2), mu +(1)/(2), z)+(1 + 2*mu)*sqrt(z)*WhittakerM(kappa, mu, z)-(kappa + mu +(1)/(2))*WhittakerM(kappa +(1)/(2), mu +(1)/(2), z) = 0	(\[Kappa]- \[Mu]-Divide[1,2])*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]+(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa], \[Mu], z]-(\[Kappa]+ \[Mu]+Divide[1,2])*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Failed [84 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E4	${\displaystyle{\displaystyle 2\mu M_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-2\mu M_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-\sqrt{z}M_{\kappa,\mu}\left(z\right)=0}}$ 2\mu\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-2\mu\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-\sqrt{z}\WhittakerconfhyperM{\kappa}{\mu}@{z} = 0		2*mu*WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)- 2*mu*WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)-sqrt(z)*WhittakerM(kappa, mu, z) = 0	2*\[Mu]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]- 2*\[Mu]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]-Sqrt[z]*WhittakerM[\[Kappa], \[Mu], z] == 0	Successful	Failure	-	Failed [78 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E5	${\displaystyle{\displaystyle 2\mu(1+2\mu)M_{\kappa,\mu}\left(z\right)-2\mu(1+2\mu)\sqrt{z}M_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-(\kappa-\mu-\tfrac{1}{2})\sqrt{z}M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ 2\mu(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}-2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-(\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		2*mu*(1 + 2*mu)*WhittakerM(kappa, mu, z)- 2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)-(kappa - mu -(1)/(2))*sqrt(z)*WhittakerM(kappa -(1)/(2), mu +(1)/(2), z) = 0	2*\[Mu]*(1 + 2*\[Mu])*WhittakerM[\[Kappa], \[Mu], z]- 2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]-(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Failed [81 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E6	${\displaystyle{\displaystyle 2\mu(1+2\mu)\sqrt{z}M_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)+(z-2\mu)(1+2\mu)M_{\kappa,\mu}\left(z\right)+(\kappa-\mu-\tfrac{1}{2})\sqrt{z}M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ 2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}+(z-2\mu)(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)+(z - 2*mu)*(1 + 2*mu)*WhittakerM(kappa, mu, z)+(kappa - mu -(1)/(2))*sqrt(z)*WhittakerM(kappa -(1)/(2), mu +(1)/(2), z) = 0	2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]+(z - 2*\[Mu])*(1 + 2*\[Mu])*WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Failed [81 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E7	${\displaystyle{\displaystyle 2\mu(1+2\mu)\sqrt{z}M_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-2\mu(1+2\mu)M_{\kappa,\mu}\left(z\right)+(\kappa+\mu+\tfrac{1}{2})\sqrt{z}M_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ 2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-2\mu(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa+\mu+\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)- 2*mu*(1 + 2*mu)*WhittakerM(kappa, mu, z)+(kappa + mu +(1)/(2))*sqrt(z)*WhittakerM(kappa +(1)/(2), mu +(1)/(2), z) = 0	2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]- 2*\[Mu]*(1 + 2*\[Mu])*WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]+Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Failed [81 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -0.5]} ... skip entries to safe data
13.15.E8	${\displaystyle{\displaystyle W_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)-\sqrt{z}W_{\kappa,\mu}\left(z\right)+(\kappa-\mu-\tfrac{1}{2})W_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ \WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z}-\sqrt{z}\WhittakerconfhyperW{\kappa}{\mu}@{z}+(\kappa-\mu-\tfrac{1}{2})\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		WhittakerW(kappa +(1)/(2), mu +(1)/(2), z)-sqrt(z)*WhittakerW(kappa, mu, z)+(kappa - mu -(1)/(2))*WhittakerW(kappa -(1)/(2), mu +(1)/(2), z) = 0	WhittakerW[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]-Sqrt[z]*WhittakerW[\[Kappa], \[Mu], z]+(\[Kappa]- \[Mu]-Divide[1,2])*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Successful [Tested: 300]
13.15.E9	${\displaystyle{\displaystyle W_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-\sqrt{z}W_{\kappa,\mu}\left(z\right)+(\kappa+\mu-\tfrac{1}{2})W_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)=0}}$ \WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-\sqrt{z}\WhittakerconfhyperW{\kappa}{\mu}@{z}+(\kappa+\mu-\tfrac{1}{2})\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0		WhittakerW(kappa +(1)/(2), mu -(1)/(2), z)-sqrt(z)*WhittakerW(kappa, mu, z)+(kappa + mu -(1)/(2))*WhittakerW(kappa -(1)/(2), mu -(1)/(2), z) = 0	WhittakerW[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]-Sqrt[z]*WhittakerW[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]-Divide[1,2])*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z] == 0	Successful	Failure	-	Successful [Tested: 300]
13.15.E10	${\displaystyle{\displaystyle 2\mu W_{\kappa,\mu}\left(z\right)-\sqrt{z}W_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)+\sqrt{z}W_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)=0}}$ 2\mu\WhittakerconfhyperW{\kappa}{\mu}@{z}-\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z}+\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0		2*mu*WhittakerW(kappa, mu, z)-sqrt(z)*WhittakerW(kappa +(1)/(2), mu +(1)/(2), z)+sqrt(z)*WhittakerW(kappa +(1)/(2), mu -(1)/(2), z) = 0	2*\[Mu]*WhittakerW[\[Kappa], \[Mu], z]-Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]+Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z] == 0	Successful	Failure	-	Successful [Tested: 300]
13.15.E11	${\displaystyle{\displaystyle W_{\kappa+1,\mu}\left(z\right)+(2\kappa-z)W_{\kappa,\mu}\left(z\right)+(\kappa-\mu-\tfrac{1}{2})(\kappa+\mu-\tfrac{1}{2})W_{\kappa-1,\mu}\left(z\right)=0}}$ \WhittakerconfhyperW{\kappa+1}{\mu}@{z}+(2\kappa-z)\WhittakerconfhyperW{\kappa}{\mu}@{z}+(\kappa-\mu-\tfrac{1}{2})(\kappa+\mu-\tfrac{1}{2})\WhittakerconfhyperW{\kappa-1}{\mu}@{z} = 0		WhittakerW(kappa + 1, mu, z)+(2*kappa - z)*WhittakerW(kappa, mu, z)+(kappa - mu -(1)/(2))*(kappa + mu -(1)/(2))*WhittakerW(kappa - 1, mu, z) = 0	WhittakerW[\[Kappa]+ 1, \[Mu], z]+(2*\[Kappa]- z)*WhittakerW[\[Kappa], \[Mu], z]+(\[Kappa]- \[Mu]-Divide[1,2])*(\[Kappa]+ \[Mu]-Divide[1,2])*WhittakerW[\[Kappa]- 1, \[Mu], z] == 0	Successful	Successful	-	Successful [Tested: 300]
13.15.E12	${\displaystyle{\displaystyle(\kappa-\mu-\tfrac{1}{2})\sqrt{z}W_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)+2\mu W_{\kappa,\mu}\left(z\right)-(\kappa+\mu-\tfrac{1}{2})\sqrt{z}W_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)=0}}$ (\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z}+2\mu\WhittakerconfhyperW{\kappa}{\mu}@{z}-(\kappa+\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0		(kappa - mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)+ 2*mu*WhittakerW(kappa, mu, z)-(kappa + mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu -(1)/(2), z) = 0	(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]+ 2*\[Mu]*WhittakerW[\[Kappa], \[Mu], z]-(\[Kappa]+ \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z] == 0	Successful	Failure	-	Successful [Tested: 300]
13.15.E13	${\displaystyle{\displaystyle(\kappa+\mu-\tfrac{1}{2})\sqrt{z}W_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-(z+2\mu)W_{\kappa,\mu}\left(z\right)+\sqrt{z}W_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$ (\kappa+\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-(z+2\mu)\WhittakerconfhyperW{\kappa}{\mu}@{z}+\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0		(kappa + mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu -(1)/(2), z)-(z + 2*mu)*WhittakerW(kappa, mu, z)+sqrt(z)*WhittakerW(kappa +(1)/(2), mu +(1)/(2), z) = 0	(\[Kappa]+ \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]-(z + 2*\[Mu])*WhittakerW[\[Kappa], \[Mu], z]+Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z] == 0	Successful	Failure	-	Successful [Tested: 300]
13.15.E14	${\displaystyle{\displaystyle(\kappa-\mu-\tfrac{1}{2})\sqrt{z}W_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)-(z-2\mu)W_{\kappa,\mu}\left(z\right)+\sqrt{z}W_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)=0}}$ (\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z}-(z-2\mu)\WhittakerconfhyperW{\kappa}{\mu}@{z}+\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0		(kappa - mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)-(z - 2*mu)*WhittakerW(kappa, mu, z)+sqrt(z)*WhittakerW(kappa +(1)/(2), mu -(1)/(2), z) = 0	(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]-(z - 2*\[Mu])*WhittakerW[\[Kappa], \[Mu], z]+Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z] == 0	Successful	Failure	-	Successful [Tested: 300]
13.15.E15	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{\left(-2\mu\right)_{n}}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}M_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{-2\mu}{n}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperM{\kappa-\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}		diff(exp((1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)]) = (- 1)^(n)* pochhammer(- 2*mu, n)*exp((1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerM(kappa -(1)/(2)*n, mu -(1)/(2)*n, z)	D[Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)* Pochhammer[- 2*\[Mu], n]*Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]-Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [210 / 300] Result: DirectedInfinity[] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: DirectedInfinity[] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E16	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}M_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = \frac{\Pochhammersym{\frac{1}{2}+\mu-\kappa}{n}}{\Pochhammersym{1+2\mu}{n}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperM{\kappa-\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}		diff(exp((1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)]) = (pochhammer((1)/(2)+ mu - kappa, n))/(pochhammer(1 + 2*mu, n))*exp((1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerM(kappa -(1)/(2)*n, mu +(1)/(2)*n, z)	D[Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}] == Divide[Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n],Pochhammer[1 + 2*\[Mu], n]]*Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]-Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [210 / 300] Result: DirectedInfinity[] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: DirectedInfinity[] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E17	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}\left(e^{\frac{1}{2}z}z^{-\kappa-1}M_{\kappa,\mu}\left(z\right)\right)={\left(\tfrac{1}{2}+\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{n-\kappa-1}M_{\kappa-n,\mu}\left(z\right)}}$ \left(z\deriv{}{z}z\right)^{n}\left(e^{\frac{1}{2}z}z^{-\kappa-1}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = \Pochhammersym{\tfrac{1}{2}+\mu-\kappa}{n}e^{\frac{1}{2}z}z^{n-\kappa-1}\WhittakerconfhyperM{\kappa-n}{\mu}@{z}		(z*diff(z, z))^(n)*(exp((1)/(2)*z)*(z)^(- kappa - 1)* WhittakerM(kappa, mu, z)) = pochhammer((1)/(2)+ mu - kappa, n)*exp((1)/(2)*z)*(z)^(n - kappa - 1)* WhittakerM(kappa - n, mu, z)	(z*D[z, z])^(n)*(Exp[Divide[1,2]*z]*(z)^(- \[Kappa]- 1)* WhittakerM[\[Kappa], \[Mu], z]) == Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(n - \[Kappa]- 1)* WhittakerM[\[Kappa]- n, \[Mu], z]	Failure	Failure	Failed [300 / 300] Result: .3585110760+.454218427e-1*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.1773224730-.5602797385*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.35851107533499493, 0.045421842889073805] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.1773224737195902, -0.560279739303586] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.15.E18	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{\left(-2\mu\right)_{n}}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}M_{\kappa+\frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{-2\mu}{n}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperM{\kappa+\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}		diff(exp(-(1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)]) = (- 1)^(n)* pochhammer(- 2*mu, n)*exp(-(1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerM(kappa +(1)/(2)*n, mu -(1)/(2)*n, z)	D[Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)* Pochhammer[- 2*\[Mu], n]*Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]+Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [210 / 300] Result: DirectedInfinity[] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: DirectedInfinity[] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E19	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}\frac{{\left(\frac{1}{2}+\mu+\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*M_{\kappa+\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = (-1)^{n}\frac{\Pochhammersym{\frac{1}{2}+\mu+\kappa}{n}}{\Pochhammersym{1+2\mu}{n}}e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*\WhittakerconfhyperM{\kappa+\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}		diff(exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)]) = (- 1)^(n)*(pochhammer((1)/(2)+ mu + kappa, n))/(pochhammer(1 + 2*mu, n))*exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerM(kappa +(1)/(2)*n, mu +(1)/(2)*n, z)	D[Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)*Divide[Pochhammer[Divide[1,2]+ \[Mu]+ \[Kappa], n],Pochhammer[1 + 2*\[Mu], n]]*Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]+Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [210 / 300] Result: DirectedInfinity[] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: DirectedInfinity[] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E20	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}M_{\kappa,\mu}\left(z\right)\right)={\left(\tfrac{1}{2}+\mu+\kappa\right)_{n}}e^{-\frac{1}{2}z}z^{\kappa+n-1}\*M_{\kappa+n,\mu}\left(z\right)}}$ \left(z\deriv{}{z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = \Pochhammersym{\tfrac{1}{2}+\mu+\kappa}{n}e^{-\frac{1}{2}z}z^{\kappa+n-1}\*\WhittakerconfhyperM{\kappa+n}{\mu}@{z}		(z*diff(z, z))^(n)*(exp(-(1)/(2)*z)*(z)^(kappa - 1)* WhittakerM(kappa, mu, z)) = pochhammer((1)/(2)+ mu + kappa, n)*exp(-(1)/(2)*z)*(z)^(kappa + n - 1)* WhittakerM(kappa + n, mu, z)	(z*D[z, z])^(n)*(Exp[-Divide[1,2]*z]*(z)^(\[Kappa]- 1)* WhittakerM[\[Kappa], \[Mu], z]) == Pochhammer[Divide[1,2]+ \[Mu]+ \[Kappa], n]*Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ n - 1)* WhittakerM[\[Kappa]+ n, \[Mu], z]	Failure	Failure	Failed [300 / 300] Result: -.221105652e-1-.2375136134*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1} Result: .3191037849-.7838469226*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.02211056528532032, -0.23751361332195844] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.31910378464483535, -0.7838469223028885] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.15.E21	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{\left(\tfrac{1}{2}+\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*W_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{\tfrac{1}{2}+\mu-\kappa}{n}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*\WhittakerconfhyperW{\kappa-\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}		diff(exp((1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)]) = (- 1)^(n)* pochhammer((1)/(2)+ mu - kappa, n)*exp((1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerW(kappa -(1)/(2)*n, mu +(1)/(2)*n, z)	D[Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)* Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]-Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [192 / 300] Result: Plus[Complex[-2.7003415598242593, -2.135803172450526], DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], Times[-1, -1.5]]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[1, 2], Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2],<syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.8050385267502765, -1.4779965316225212], Times[2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], Times[-1, -1.5]]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[1, 2], Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], Times[-1, -1.5]]], Plus[Times[-1, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, -1.5, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, WhittakerW[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]]}]][2.0]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E22	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{\left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\*W_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{\tfrac{1}{2}-\mu-\kappa}{n}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\*\WhittakerconfhyperW{\kappa-\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}		diff(exp((1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)]) = (- 1)^(n)* pochhammer((1)/(2)- mu - kappa, n)*exp((1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerW(kappa -(1)/(2)*n, mu -(1)/(2)*n, z)	D[Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)* Pochhammer[Divide[1,2]- \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]-Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [192 / 300] Result: Plus[Complex[-3.1506729340368813, -11.027912097410434], DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], -1.5]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[1, 2], Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], -1.5]], P<syntaxhighlight lang=mathematica>Result: Plus[Complex[32.491056912593166, 25.892568815057246], Times[2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[-1, Times[-2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], -1.5]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[1, 2], Power[E, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], -1.5]], Plus[Times[-1, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[2, -1.5, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, WhittakerW[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]]}]][2.0]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E23	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}\left(e^{\frac{1}{2}z}z^{-\kappa-1}W_{\kappa,\mu}\left(z\right)\right)={\left(\tfrac{1}{2}+\mu-\kappa\right)_{n}}{\left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{n-\kappa-1}W_{\kappa-n,\mu}\left(z\right)}}$ \left(z\deriv{}{z}z\right)^{n}\left(e^{\frac{1}{2}z}z^{-\kappa-1}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = \Pochhammersym{\tfrac{1}{2}+\mu-\kappa}{n}\Pochhammersym{\tfrac{1}{2}-\mu-\kappa}{n}e^{\frac{1}{2}z}z^{n-\kappa-1}\WhittakerconfhyperW{\kappa-n}{\mu}@{z}		(z*diff(z, z))^(n)*(exp((1)/(2)*z)*(z)^(- kappa - 1)* WhittakerW(kappa, mu, z)) = pochhammer((1)/(2)+ mu - kappa, n)*pochhammer((1)/(2)- mu - kappa, n)*exp((1)/(2)*z)*(z)^(n - kappa - 1)* WhittakerW(kappa - n, mu, z)	(z*D[z, z])^(n)*(Exp[Divide[1,2]*z]*(z)^(- \[Kappa]- 1)* WhittakerW[\[Kappa], \[Mu], z]) == Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n]*Pochhammer[Divide[1,2]- \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(n - \[Kappa]- 1)* WhittakerW[\[Kappa]- n, \[Mu], z]	Failure	Failure	Failed [300 / 300] Result: 2.468472246+1.546856952*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1} Result: 1.885026449+1.175257266*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[2.4684722428383408, 1.546856950437671] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.8850264475606715, 1.175257265810332] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.15.E24	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}W_{\kappa+\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperW{\kappa+\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}		diff(exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)]) = (- 1)^(n)* exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerW(kappa +(1)/(2)*n, mu +(1)/(2)*n, z)	D[Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]+Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [192 / 300] Result: Plus[Complex[0.5001431347806349, -0.3406797899835502], DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[1, Times[2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], Times[-1, -1.5]]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[-1, 2], Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], Times[-1, <syntaxhighlight lang=mathematica>Result: Plus[Complex[0.332118444019996, 0.20129597063218943], Times[2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[1, Times[2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], Times[-1, -1.5]]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[-1, 2], Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], Times[-1, -1.5]]], Plus[WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[2, -1.5, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[2, WhittakerW[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]]}]][2.0]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E25	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}W_{\kappa+\frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$ \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperW{\kappa+\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}		diff(exp(-(1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)]) = (- 1)^(n)* exp(-(1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerW(kappa +(1)/(2)*n, mu -(1)/(2)*n, z)	D[Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}] == (- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]+Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z]	Failure	Failure	Skipped - Because timed out	Failed [192 / 300] Result: Plus[Complex[-3.483681927072143, -5.36298237509452], DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[1, Times[2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], -1.5]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[1, 2], Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], -1.5]], Plus[Times[-1,<syntaxhighlight lang=mathematica>Result: Plus[Complex[24.085306751162083, 11.80402713986923], Times[2.0, DifferenceRoot[Function[{, } Test Values: {Equal[Plus[Times[Plus[1, Times[2, ], Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, -1.5]], []], Times[2, Plus[1, ], Plus[1, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[-2, -1.5]], [Plus[1, ]]], Times[2, Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[2, ]]]], 0], Equal[[0], Times[Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-1, 2], -1.5]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[1], Times[Rational[1, 2], Power[E, Times[Rational[-1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[Rational[-3, 2], -1.5]], Plus[Times[-1, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[2, -1.5, WhittakerW[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[-2, WhittakerW[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]]}]][2.0]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} ... skip entries to safe data
13.15.E26	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}e^{-\frac{1}{2}z}z^{\kappa+n-1}W_{\kappa+n,\mu}\left(z\right)}}$ \left(z\deriv{}{z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}e^{-\frac{1}{2}z}z^{\kappa+n-1}\WhittakerconfhyperW{\kappa+n}{\mu}@{z}		(z*diff(z, z))^(n)*(exp(-(1)/(2)*z)*(z)^(kappa - 1)* WhittakerW(kappa, mu, z)) = (- 1)^(n)* exp(-(1)/(2)*z)*(z)^(kappa + n - 1)* WhittakerW(kappa + n, mu, z)	(z*D[z, z])^(n)*(Exp[-Divide[1,2]*z]*(z)^(\[Kappa]- 1)* WhittakerW[\[Kappa], \[Mu], z]) == (- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ n - 1)* WhittakerW[\[Kappa]+ n, \[Mu], z]	Failure	Failure	Failed [300 / 300] Result: .2623016537+.1488103823*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1} Result: .1952811915+.4851862634*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.26230165366126323, 0.1488103820981603] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.1952811914323972, 0.4851862632402242] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.16.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+2\mu\right)z^{\mu+\frac{1}{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*\int_{-1}^{1}e^{\frac{1}{2}zt}(1+t)^{\mu-\frac{1}{2}-\kappa}(1-t)^{\mu-\frac{1}{2}+\kappa}\mathrm{d}t}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\EulerGamma@{1+2\mu}z^{\mu+\frac{1}{2}}2^{-2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\*\int_{-1}^{1}e^{\frac{1}{2}zt}(1+t)^{\mu-\frac{1}{2}-\kappa}(1-t)^{\mu-\frac{1}{2}+\kappa}\diff{t}	${\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\left|\Re\kappa\right|,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}+\mu+\kappa)>0}}$	WhittakerM(kappa, mu, z) = (GAMMA(1 + 2*mu)*(z)^(mu +(1)/(2))* (2)^(- 2*mu))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)+ mu + kappa))* int(exp((1)/(2)*z*t)*(1 + t)^(mu -(1)/(2)- kappa)*(1 - t)^(mu -(1)/(2)+ kappa), t = - 1..1)	WhittakerM[\[Kappa], \[Mu], z] == Divide[Gamma[1 + 2*\[Mu]]*(z)^(\[Mu]+Divide[1,2])* (2)^(- 2*\[Mu]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]* Integrate[Exp[Divide[1,2]*z*t]*(1 + t)^(\[Mu]-Divide[1,2]- \[Kappa])*(1 - t)^(\[Mu]-Divide[1,2]+ \[Kappa]), {t, - 1, 1}, GenerateConditions->None]	Failure	Successful	Skipped - Because timed out	Successful [Tested: 252]
13.16.E2	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+2\mu\right)z^{\lambda}}{\Gamma\left(1+2\mu-2\lambda\right)\Gamma\left(2\lambda\right)}\*\int_{0}^{1}M_{\kappa-\lambda,\mu-\lambda}\left(zt\right)e^{\frac{1}{2}z(t-1)}t^{\mu-\lambda-\frac{1}{2}}{(1-t)^{2\lambda-1}}\mathrm{d}t}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\EulerGamma@{1+2\mu}z^{\lambda}}{\EulerGamma@{1+2\mu-2\lambda}\EulerGamma@{2\lambda}}\*\int_{0}^{1}\WhittakerconfhyperM{\kappa-\lambda}{\mu-\lambda}@{zt}e^{\frac{1}{2}z(t-1)}t^{\mu-\lambda-\frac{1}{2}}{(1-t)^{2\lambda-1}}\diff{t}	${\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\Re\lambda,\Re\lambda>0,\Re(1+2\mu)>0,\Re(1+2\mu-2\lambda)>0,\Re(2\lambda)>0}}$	WhittakerM(kappa, mu, z) = (GAMMA(1 + 2*mu)*(z)^(lambda))/(GAMMA(1 + 2*mu - 2*lambda)*GAMMA(2*lambda))* int(WhittakerM(kappa - lambda, mu - lambda, z*t)*exp((1)/(2)*z*(t - 1))*(t)^(mu - lambda -(1)/(2))*(1 - t)^(2*lambda - 1), t = 0..1)	WhittakerM[\[Kappa], \[Mu], z] == Divide[Gamma[1 + 2*\[Mu]]*(z)^\[Lambda],Gamma[1 + 2*\[Mu]- 2*\[Lambda]]*Gamma[2*\[Lambda]]]* Integrate[WhittakerM[\[Kappa]- \[Lambda], \[Mu]- \[Lambda], z*t]*Exp[Divide[1,2]*z*(t - 1)]*(t)^(\[Mu]- \[Lambda]-Divide[1,2])*(1 - t)^(2*\[Lambda]- 1), {t, 0, 1}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.16.E3	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=\frac{\sqrt{z}e^{\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\int_{0}^{\infty}e^{-t}t^{\kappa-\frac{1}{2}}J_{2\mu}\left(2\sqrt{zt}\right)\mathrm{d}t}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\sqrt{z}e^{\frac{1}{2}z}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\int_{0}^{\infty}e^{-t}t^{\kappa-\frac{1}{2}}\BesselJ{2\mu}@{2\sqrt{zt}}\diff{t}	${\displaystyle{\displaystyle\Re\left(\kappa+\mu\right)+\tfrac{1}{2}>0,\Re((2\mu)+k+1)>0,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z) = (sqrt(z)*exp((1)/(2)*z))/(GAMMA((1)/(2)+ mu + kappa))*int(exp(- t)*(t)^(kappa -(1)/(2))* BesselJ(2*mu, 2*sqrt(z*t)), t = 0..infinity)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z] == Divide[Sqrt[z]*Exp[Divide[1,2]*z],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*Integrate[Exp[- t]*(t)^(\[Kappa]-Divide[1,2])* BesselJ[2*\[Mu], 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]	Successful	Aborted	-	Skipped - Because timed out
13.16.E4	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=\frac{\sqrt{z}e^{-\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}I_{2\mu}\left(2\sqrt{zt}\right)\mathrm{d}t}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\sqrt{z}e^{-\frac{1}{2}z}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}\modBesselI{2\mu}@{2\sqrt{zt}}\diff{t}	${\displaystyle{\displaystyle\Re(\kappa-\mu)-\tfrac{1}{2}<0,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re((2\mu)+k+1)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z) = (sqrt(z)*exp(-(1)/(2)*z))/(GAMMA((1)/(2)+ mu - kappa))* int(exp(- t)*(t)^(- kappa -(1)/(2))* BesselI(2*mu, 2*sqrt(z*t)), t = 0..infinity)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z] == Divide[Sqrt[z]*Exp[-Divide[1,2]*z],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Exp[- t]*(t)^(- \[Kappa]-Divide[1,2])* BesselI[2*\[Mu], 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]	Failure	Successful	Failed [42 / 300] Result: .5483729950e-2+.5411197480e-1*I Test Values: {kappa = -3/2, mu = 2, z = 1/2*3^(1/2)+1/2*I} Result: .2482822497e-1-.2550894001e-1*I Test Values: {kappa = -3/2, mu = 2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Successful [Tested: 300]
13.16.E5	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{z^{\mu+\frac{1}{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{1}^{\infty}e^{-\frac{1}{2}zt}(t-1)^{\mu-\frac{1}{2}-\kappa}(t+1)^{\mu-\frac{1}{2}+\kappa}\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{z^{\mu+\frac{1}{2}}2^{-2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{1}^{\infty}e^{-\frac{1}{2}zt}(t-1)^{\mu-\frac{1}{2}-\kappa}(t+1)^{\mu-\frac{1}{2}+\kappa}\diff{t}	${\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\Re\kappa,|\operatorname{ph}{z}|<\frac{1}{2}\pi,\Re(\frac{1}{2}+\mu-\kappa)>0}}$	WhittakerW(kappa, mu, z) = ((z)^(mu +(1)/(2))* (2)^(- 2*mu))/(GAMMA((1)/(2)+ mu - kappa))* int(exp(-(1)/(2)*z*t)*(t - 1)^(mu -(1)/(2)- kappa)*(t + 1)^(mu -(1)/(2)+ kappa), t = 1..infinity)	WhittakerW[\[Kappa], \[Mu], z] == Divide[(z)^(\[Mu]+Divide[1,2])* (2)^(- 2*\[Mu]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Exp[-Divide[1,2]*z*t]*(t - 1)^(\[Mu]-Divide[1,2]- \[Kappa])*(t + 1)^(\[Mu]-Divide[1,2]+ \[Kappa]), {t, 1, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 300]
13.16.E6	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2}z}z^{\kappa+1}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{W_{-\kappa,\mu}\left(t\right)e^{-\frac{1}{2}t}t^{-\kappa-1}}{t+z}\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{e^{-\frac{1}{2}z}z^{\kappa+1}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\*\int_{0}^{\infty}\frac{\WhittakerconfhyperW{-\kappa}{\mu}@{t}e^{-\frac{1}{2}t}t^{-\kappa-1}}{t+z}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\pi,\Re\left(\frac{1}{2}+\mu-\kappa\right)>\max\left(2\Re\mu,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}\)\@add@PDF@RDFa@triples\end{document}}$	WhittakerW(kappa, mu, z) = (exp(-(1)/(2)*z)*(z)^(kappa + 1))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))* int((WhittakerW(- kappa, mu, t)*exp(-(1)/(2)*t)*(t)^(- kappa - 1))/(t + z), t = 0..infinity)	WhittakerW[\[Kappa], \[Mu], z] == Divide[Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ 1),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]* Integrate[Divide[WhittakerW[- \[Kappa], \[Mu], t]*Exp[-Divide[1,2]*t]*(t)^(- \[Kappa]- 1),t + z], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Manual Skip!	Successful [Tested: 300]
13.16.E7	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}-\mu-n}}{\Gamma\left(1+2\mu\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{M_{-\kappa,\mu}\left(t\right)e^{-\frac{1}{2}t}t^{n+\mu-\frac{1}{2}}}{t+z}\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}-\mu-n}}{\EulerGamma@{1+2\mu}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\*\int_{0}^{\infty}\frac{\WhittakerconfhyperM{-\kappa}{\mu}@{t}e^{-\frac{1}{2}t}t^{n+\mu-\frac{1}{2}}}{t+z}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi,-\Re\left(1+2\mu\right)<n,n<\left|\Re\mu\right|+\Re\kappa,\left|\Re\mu\right|+\Re\kappa<\tfrac{1}{2},\Re(1+2\mu)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	WhittakerW(kappa, mu, z) = ((- 1)^(n)* exp(-(1)/(2)*z)*(z)^((1)/(2)- mu - n))/(GAMMA(1 + 2*mu)*GAMMA((1)/(2)- mu - kappa))* int((WhittakerM(- kappa, mu, t)*exp(-(1)/(2)*t)*(t)^(n + mu -(1)/(2)))/(t + z), t = 0..infinity)	WhittakerW[\[Kappa], \[Mu], z] == Divide[(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]- \[Mu]- n),Gamma[1 + 2*\[Mu]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]* Integrate[Divide[WhittakerM[- \[Kappa], \[Mu], t]*Exp[-Divide[1,2]*t]*(t)^(n + \[Mu]-Divide[1,2]),t + z], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
13.16.E8	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{2\sqrt{z}e^{-\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}K_{2\mu}\left(2\sqrt{zt}\right)\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{2\sqrt{z}e^{-\frac{1}{2}z}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}\modBesselK{2\mu}@{2\sqrt{zt}}\diff{t}	${\displaystyle{\displaystyle\Re\left(\mu-\kappa\right)+\tfrac{1}{2}>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	WhittakerW(kappa, mu, z) = (2*sqrt(z)*exp(-(1)/(2)*z))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))* int(exp(- t)*(t)^(- kappa -(1)/(2))* BesselK(2*mu, 2*sqrt(z*t)), t = 0..infinity)	WhittakerW[\[Kappa], \[Mu], z] == Divide[2*Sqrt[z]*Exp[-Divide[1,2]*z],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]* Integrate[Exp[- t]*(t)^(- \[Kappa]-Divide[1,2])* BesselK[2*\[Mu], 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]	Successful	Aborted	-	Successful [Tested: 252]
13.16.E9	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{\kappa+c}\*\int_{0}^{\infty}e^{-zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left({\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}-\mu-\kappa\atop c};-t\right)\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\kappa+c}\*\int_{0}^{\infty}e^{-zt}t^{c-1}\genhyperOlverF{2}{1}@@{\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}-\mu-\kappa}{c}{-t}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}$	WhittakerW(kappa, mu, z) = exp(-(1)/(2)*z)*(z)^(kappa + c)* int(exp(- z*t)*(t)^(c - 1)* hypergeom([(1)/(2)+ mu - kappa ,(1)/(2)- mu - kappa], [c], - t), t = 0..infinity)	WhittakerW[\[Kappa], \[Mu], z] == Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ c)* Integrate[Exp[- z*t]*(t)^(c - 1)* HypergeometricPFQRegularized[{Divide[1,2]+ \[Mu]- \[Kappa],Divide[1,2]- \[Mu]- \[Kappa]}, {c}, - t], {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
13.16.E10	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)=\frac{e^{\frac{1}{2}z+(\frac{1}{2}+\mu)\pi\mathrm{i}}}{2\pi\mathrm{i}\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(t-\kappa\right)\Gamma\left(\frac{1}{2}+\mu-t\right)}{\Gamma\left(\frac{1}{2}+\mu+t\right)}z^{t}\mathrm{d}t}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{e^{+\pi\iunit}z} = \frac{e^{\frac{1}{2}z+(\frac{1}{2}+\mu)\pi\iunit}}{2\pi\iunit\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{t-\kappa}\EulerGamma@{\frac{1}{2}+\mu-t}}{\EulerGamma@{\frac{1}{2}+\mu+t}}z^{t}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(t-\kappa)>0,\Re(\frac{1}{2}+\mu-t)>0,\Re(\frac{1}{2}+\mu+t)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, exp(+ Pi*I)*z) = (exp((1)/(2)*z +((1)/(2)+ mu)*Pi*I))/(2*Pi*I*GAMMA((1)/(2)+ mu - kappa))* int((GAMMA(t - kappa)*GAMMA((1)/(2)+ mu - t))/(GAMMA((1)/(2)+ mu + t))*(z)^(t), t = - I*infinity..I*infinity)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], Exp[+ Pi*I]*z] == Divide[Exp[Divide[1,2]*z +(Divide[1,2]+ \[Mu])*Pi*I],2*Pi*I*Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Divide[Gamma[t - \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]- t],Gamma[Divide[1,2]+ \[Mu]+ t]]*(z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.16.E10	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)=\frac{e^{\frac{1}{2}z-(\frac{1}{2}+\mu)\pi\mathrm{i}}}{2\pi\mathrm{i}\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(t-\kappa\right)\Gamma\left(\frac{1}{2}+\mu-t\right)}{\Gamma\left(\frac{1}{2}+\mu+t\right)}z^{t}\mathrm{d}t}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{e^{-\pi\iunit}z} = \frac{e^{\frac{1}{2}z-(\frac{1}{2}+\mu)\pi\iunit}}{2\pi\iunit\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{t-\kappa}\EulerGamma@{\frac{1}{2}+\mu-t}}{\EulerGamma@{\frac{1}{2}+\mu+t}}z^{t}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(t-\kappa)>0,\Re(\frac{1}{2}+\mu-t)>0,\Re(\frac{1}{2}+\mu+t)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, exp(- Pi*I)*z) = (exp((1)/(2)*z -((1)/(2)+ mu)*Pi*I))/(2*Pi*I*GAMMA((1)/(2)+ mu - kappa))* int((GAMMA(t - kappa)*GAMMA((1)/(2)+ mu - t))/(GAMMA((1)/(2)+ mu + t))*(z)^(t), t = - I*infinity..I*infinity)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], Exp[- Pi*I]*z] == Divide[Exp[Divide[1,2]*z -(Divide[1,2]+ \[Mu])*Pi*I],2*Pi*I*Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Divide[Gamma[t - \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]- t],Gamma[Divide[1,2]+ \[Mu]+ t]]*(z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.16.E11	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2}z}}{2\pi\mathrm{i}}\*\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(\frac{1}{2}+\mu+t\right)\Gamma\left(\frac{1}{2}-\mu+t\right)\Gamma\left(-\kappa-t\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}z^{-t}\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{e^{-\frac{1}{2}z}}{2\pi\iunit}\*\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{\frac{1}{2}+\mu+t}\EulerGamma@{\frac{1}{2}-\mu+t}\EulerGamma@{-\kappa-t}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}z^{-t}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{3}{2}\pi,\Re(\frac{1}{2}+\mu+t)>0,\Re(\frac{1}{2}-\mu+t)>0,\Re(-\kappa-t)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	WhittakerW(kappa, mu, z) = (exp(-(1)/(2)*z))/(2*Pi*I)* int((GAMMA((1)/(2)+ mu + t)*GAMMA((1)/(2)- mu + t)*GAMMA(- kappa - t))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))*(z)^(- t), t = - I*infinity..I*infinity)	WhittakerW[\[Kappa], \[Mu], z] == Divide[Exp[-Divide[1,2]*z],2*Pi*I]* Integrate[Divide[Gamma[Divide[1,2]+ \[Mu]+ t]*Gamma[Divide[1,2]- \[Mu]+ t]*Gamma[- \[Kappa]- t],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*(z)^(- t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.16.E12	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{\frac{1}{2}z}}{2\pi\mathrm{i}}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(\frac{1}{2}+\mu+t\right)\Gamma\left(\frac{1}{2}-\mu+t\right)}{\Gamma\left(1-\kappa+t\right)}z^{-t}\mathrm{d}t}}$ \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{e^{\frac{1}{2}z}}{2\pi\iunit}\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{\frac{1}{2}+\mu+t}\EulerGamma@{\frac{1}{2}-\mu+t}}{\EulerGamma@{1-\kappa+t}}z^{-t}\diff{t}	${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi,\Re(\frac{1}{2}+\mu+t)>0,\Re(\frac{1}{2}-\mu+t)>0,\Re(1-\kappa+t)>0}}$	WhittakerW(kappa, mu, z) = (exp((1)/(2)*z))/(2*Pi*I)*int((GAMMA((1)/(2)+ mu + t)*GAMMA((1)/(2)- mu + t))/(GAMMA(1 - kappa + t))*(z)^(- t), t = - I*infinity..I*infinity)	WhittakerW[\[Kappa], \[Mu], z] == Divide[Exp[Divide[1,2]*z],2*Pi*I]*Integrate[Divide[Gamma[Divide[1,2]+ \[Mu]+ t]*Gamma[Divide[1,2]- \[Mu]+ t],Gamma[1 - \[Kappa]+ t]]*(z)^(- t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.18.E1	${\displaystyle{\displaystyle M_{0,\frac{1}{2}}\left(2z\right)=2\sinh z}}$ \WhittakerconfhyperM{0}{\frac{1}{2}}@{2z} = 2\sinh@@{z}		WhittakerM(0, (1)/(2), 2*z) = 2*sinh(z)	WhittakerM[0, Divide[1,2], 2*z] == 2*Sinh[z]	Successful	Successful	-	Successful [Tested: 7]
13.18.E2	${\displaystyle{\displaystyle M_{\kappa,\kappa-\frac{1}{2}}\left(z\right)=W_{\kappa,\kappa-\frac{1}{2}}\left(z\right)}}$ \WhittakerconfhyperM{\kappa}{\kappa-\frac{1}{2}}@{z} = \WhittakerconfhyperW{\kappa}{\kappa-\frac{1}{2}}@{z}		WhittakerM(kappa, kappa -(1)/(2), z) = WhittakerW(kappa, kappa -(1)/(2), z)	WhittakerM[\[Kappa], \[Kappa]-Divide[1,2], z] == WhittakerW[\[Kappa], \[Kappa]-Divide[1,2], z]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
13.18.E2	${\displaystyle{\displaystyle W_{\kappa,\kappa-\frac{1}{2}}\left(z\right)=W_{\kappa,-\kappa+\frac{1}{2}}\left(z\right)}}$ \WhittakerconfhyperW{\kappa}{\kappa-\frac{1}{2}}@{z} = \WhittakerconfhyperW{\kappa}{-\kappa+\frac{1}{2}}@{z}		WhittakerW(kappa, kappa -(1)/(2), z) = WhittakerW(kappa, - kappa +(1)/(2), z)	WhittakerW[\[Kappa], \[Kappa]-Divide[1,2], z] == WhittakerW[\[Kappa], - \[Kappa]+Divide[1,2], z]	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
13.18.E2	${\displaystyle{\displaystyle W_{\kappa,-\kappa+\frac{1}{2}}\left(z\right)=e^{-\frac{1}{2}z}z^{\kappa}}}$ \WhittakerconfhyperW{\kappa}{-\kappa+\frac{1}{2}}@{z} = e^{-\frac{1}{2}z}z^{\kappa}		WhittakerW(kappa, - kappa +(1)/(2), z) = exp(-(1)/(2)*z)*(z)^(kappa)	WhittakerW[\[Kappa], - \[Kappa]+Divide[1,2], z] == Exp[-Divide[1,2]*z]*(z)^\[Kappa]	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
13.18.E3	${\displaystyle{\displaystyle M_{\kappa,-\kappa-\frac{1}{2}}\left(z\right)=e^{\frac{1}{2}z}z^{-\kappa}}}$ \WhittakerconfhyperM{\kappa}{-\kappa-\frac{1}{2}}@{z} = e^{\frac{1}{2}z}z^{-\kappa}		WhittakerM(kappa, - kappa -(1)/(2), z) = exp((1)/(2)*z)*(z)^(- kappa)	WhittakerM[\[Kappa], - \[Kappa]-Divide[1,2], z] == Exp[Divide[1,2]*z]*(z)^(- \[Kappa])	Successful	Successful	-	Failed [20 / 70] Result: Complex[-0.012581208495203278, -0.029801099144953658] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, 1.5]} Result: Complex[-0.32783156414330006, -0.2917810845255237] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, 0.5]} ... skip entries to safe data
13.18.E4	${\displaystyle{\displaystyle M_{\mu-\frac{1}{2},\mu}\left(z\right)=2\mu e^{\frac{1}{2}z}z^{\frac{1}{2}-\mu}\gamma\left(2\mu,z\right)}}$ \WhittakerconfhyperM{\mu-\frac{1}{2}}{\mu}@{z} = 2\mu e^{\frac{1}{2}z}z^{\frac{1}{2}-\mu}\incgamma@{2\mu}{z}	${\displaystyle{\displaystyle\Re(2\mu)>0}}$	WhittakerM(mu -(1)/(2), mu, z) = 2*mu*exp((1)/(2)*z)*(z)^((1)/(2)- mu)* GAMMA(2*mu)-GAMMA(2*mu, z)	WhittakerM[\[Mu]-Divide[1,2], \[Mu], z] == 2*\[Mu]*Exp[Divide[1,2]*z]*(z)^(Divide[1,2]- \[Mu])* Gamma[2*\[Mu], 0, z]	Failure	Successful	Failed [35 / 35] Result: -.5507089801-1.429327526*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: -2.178955063-1.073512810*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Successful [Tested: 35]
13.18.E5	${\displaystyle{\displaystyle W_{\mu-\frac{1}{2},\mu}\left(z\right)=e^{\frac{1}{2}z}z^{\frac{1}{2}-\mu}\Gamma\left(2\mu,z\right)}}$ \WhittakerconfhyperW{\mu-\frac{1}{2}}{\mu}@{z} = e^{\frac{1}{2}z}z^{\frac{1}{2}-\mu}\incGamma@{2\mu}{z}		WhittakerW(mu -(1)/(2), mu, z) = exp((1)/(2)*z)*(z)^((1)/(2)- mu)* GAMMA(2*mu, z)	WhittakerW[\[Mu]-Divide[1,2], \[Mu], z] == Exp[Divide[1,2]*z]*(z)^(Divide[1,2]- \[Mu])* Gamma[2*\[Mu], z]	Successful	Successful	-	Successful [Tested: 70]
13.18.E6	${\displaystyle{\displaystyle M_{-\frac{1}{4},\frac{1}{4}}\left(z^{2}\right)=\tfrac{1}{2}e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\operatorname{erf}\left(z\right)}}$ \WhittakerconfhyperM{-\frac{1}{4}}{\frac{1}{4}}@{z^{2}} = \tfrac{1}{2}e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\erf@{z}		WhittakerM(-(1)/(4), (1)/(4), (z)^(2)) = (1)/(2)*exp((1)/(2)*(z)^(2))*sqrt(Pi*z)*erf(z)	WhittakerM[-Divide[1,4], Divide[1,4], (z)^(2)] == Divide[1,2]*Exp[Divide[1,2]*(z)^(2)]*Sqrt[Pi*z]*Erf[z]	Failure	Failure	Failed [2 / 7] Result: .7978557562-.9869289445*I Test Values: {z = -1/2+1/2*I*3^(1/2)} Result: 1.482664004+.2744150982*I Test Values: {z = -1/2*3^(1/2)-1/2*I}	Failed [2 / 7] Result: Complex[0.7978557563768727, -0.986928944338508] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[1.4826640039189691, 0.2744150979001404] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.18.E7	${\displaystyle{\displaystyle W_{-\frac{1}{4},+\frac{1}{4}}\left(z^{2}\right)=e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\operatorname{erfc}\left(z\right)}}$ \WhittakerconfhyperW{-\frac{1}{4}}{+\frac{1}{4}}@{z^{2}} = e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\erfc@{z}		WhittakerW(-(1)/(4), +(1)/(4), (z)^(2)) = exp((1)/(2)*(z)^(2))*sqrt(Pi*z)*erfc(z)	WhittakerW[-Divide[1,4], +Divide[1,4], (z)^(2)] == Exp[Divide[1,2]*(z)^(2)]*Sqrt[Pi*z]*Erfc[z]	Failure	Failure	Failed [2 / 7] Result: -1.928317415+.502368653e-1*I Test Values: {z = -1/2+1/2*I*3^(1/2)} Result: -2.674168572+2.656547698*I Test Values: {z = -1/2*3^(1/2)-1/2*I}	Failed [2 / 7] Result: Complex[-1.9283174154667808, 0.050236864945780724] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[-2.6741685713500765, 2.656547698651725] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.18.E7	${\displaystyle{\displaystyle W_{-\frac{1}{4},-\frac{1}{4}}\left(z^{2}\right)=e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\operatorname{erfc}\left(z\right)}}$ \WhittakerconfhyperW{-\frac{1}{4}}{-\frac{1}{4}}@{z^{2}} = e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\erfc@{z}		WhittakerW(-(1)/(4), -(1)/(4), (z)^(2)) = exp((1)/(2)*(z)^(2))*sqrt(Pi*z)*erfc(z)	WhittakerW[-Divide[1,4], -Divide[1,4], (z)^(2)] == Exp[Divide[1,2]*(z)^(2)]*Sqrt[Pi*z]*Erfc[z]	Failure	Failure	Failed [2 / 7] Result: -1.928317415+.502368653e-1*I Test Values: {z = -1/2+1/2*I*3^(1/2)} Result: -2.674168572+2.656547698*I Test Values: {z = -1/2*3^(1/2)-1/2*I}	Failed [2 / 7] Result: Complex[-1.928317415466781, 0.05023686494578061] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[-2.674168571350077, 2.6565476986517247] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.18.E8	${\displaystyle{\displaystyle M_{0,\nu}\left(2z\right)=2^{2\nu+\frac{1}{2}}\Gamma\left(1+\nu\right)\sqrt{z}I_{\nu}\left(z\right)}}$ \WhittakerconfhyperM{0}{\nu}@{2z} = 2^{2\nu+\frac{1}{2}}\EulerGamma@{1+\nu}\sqrt{z}\modBesselI{\nu}@{z}	${\displaystyle{\displaystyle\Re(1+\nu)>0,\Re(\nu+k+1)>0}}$	WhittakerM(0, nu, 2*z) = (2)^(2*nu +(1)/(2))* GAMMA(1 + nu)*sqrt(z)*BesselI(nu, z)	WhittakerM[0, \[Nu], 2*z] == (2)^(2*\[Nu]+Divide[1,2])* Gamma[1 + \[Nu]]*Sqrt[z]*BesselI[\[Nu], z]	Successful	Successful	-	Failed [7 / 56] Result: Complex[-0.8586367168171446, -0.6707313588072118] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]} Result: Complex[0.33759646322286985, -0.8589803343001376] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]} ... skip entries to safe data
13.18.E9	${\displaystyle{\displaystyle W_{0,\nu}\left(2z\right)=\sqrt{\ifrac{2z}{\pi}}K_{\nu}\left(z\right)}}$ \WhittakerconfhyperW{0}{\nu}@{2z} = \sqrt{\ifrac{2z}{\pi}}\modBesselK{\nu}@{z}		WhittakerW(0, nu, 2*z) = sqrt((2*z)/(Pi))*BesselK(nu, z)	WhittakerW[0, \[Nu], 2*z] == Sqrt[Divide[2*z,Pi]]*BesselK[\[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
13.18.E10	${\displaystyle{\displaystyle W_{0,\frac{1}{3}}\left(\tfrac{4}{3}z^{\frac{3}{2}}\right)=2\sqrt{\pi}z^{\frac{1}{4}}\mathrm{Ai}\left(z\right)}}$ \WhittakerconfhyperW{0}{\frac{1}{3}}@{\tfrac{4}{3}z^{\frac{3}{2}}} = 2\sqrt{\pi}z^{\frac{1}{4}}\AiryAi@{z}		WhittakerW(0, (1)/(3), (4)/(3)*(z)^((3)/(2))) = 2*sqrt(Pi)*(z)^((1)/(4))* AiryAi(z)	WhittakerW[0, Divide[1,3], Divide[4,3]*(z)^(Divide[3,2])] == 2*Sqrt[Pi]*(z)^(Divide[1,4])* AiryAi[z]	Failure	Failure	Failed [1 / 7] Result: -.246840478+.5335590044*I Test Values: {z = -1/2*3^(1/2)-1/2*I}	Failed [1 / 7] Result: Complex[-0.24684047859323988, 0.533559004293784] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.18.E12	${\displaystyle{\displaystyle M_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a-1}\Gamma\left(\tfrac{1}{2}a+\tfrac{3}{4}\right)\sqrt{\ifrac{z}{\pi}}\*\left(U\left(a,z\right)+U\left(a,-z\right)\right)}}$ \WhittakerconfhyperM{-\frac{1}{2}a}{-\frac{1}{4}}@{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a-1}\EulerGamma@{\tfrac{1}{2}a+\tfrac{3}{4}}\sqrt{\ifrac{z}{\pi}}\*\left(\paraU@{a}{z}+\paraU@{a}{-z}\right)	${\displaystyle{\displaystyle\Re(\tfrac{1}{2}a+\tfrac{3}{4})>0}}$	WhittakerM(-(1)/(2)*a, -(1)/(4), (1)/(2)*(z)^(2)) = (2)^((1)/(2)*a - 1)* GAMMA((1)/(2)*a +(3)/(4))*sqrt((z)/(Pi))*(CylinderU(a, z)+ CylinderU(a, - z))	WhittakerM[-Divide[1,2]*a, -Divide[1,4], Divide[1,2]*(z)^(2)] == (2)^(Divide[1,2]*a - 1)* Gamma[Divide[1,2]*a +Divide[3,4]]*Sqrt[Divide[z,Pi]]*(ParabolicCylinderD[- 1/2 -(a), z]+ ParabolicCylinderD[- 1/2 -(a), - z])	Failure	Failure	Failed [8 / 28] Result: -.4546011384-.8349579092*I Test Values: {a = 3/2, z = -1/2+1/2*I*3^(1/2)} Result: .58169427e-2+1.789104086*I Test Values: {a = 3/2, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [8 / 28] Result: Complex[-0.454601138107828, -0.8349579095614801] Test Values: {Rule[a, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[0.005816942543956816, 1.7891040854776739] Test Values: {Rule[a, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data
13.18.E13	${\displaystyle{\displaystyle M_{-\frac{1}{2}a,\frac{1}{4}}\left(\tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a-2}\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{4}\right)\sqrt{\ifrac{z}{\pi}}\*\left(U\left(a,-z\right)-U\left(a,z\right)\right)}}$ \WhittakerconfhyperM{-\frac{1}{2}a}{\frac{1}{4}}@{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a-2}\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{4}}\sqrt{\ifrac{z}{\pi}}\*\left(\paraU@{a}{-z}-\paraU@{a}{z}\right)	${\displaystyle{\displaystyle\Re(\tfrac{1}{2}a+\tfrac{1}{4})>0}}$	WhittakerM(-(1)/(2)*a, (1)/(4), (1)/(2)*(z)^(2)) = (2)^((1)/(2)*a - 2)* GAMMA((1)/(2)*a +(1)/(4))*sqrt((z)/(Pi))*(CylinderU(a, - z)- CylinderU(a, z))	WhittakerM[-Divide[1,2]*a, Divide[1,4], Divide[1,2]*(z)^(2)] == (2)^(Divide[1,2]*a - 2)* Gamma[Divide[1,2]*a +Divide[1,4]]*Sqrt[Divide[z,Pi]]*(ParabolicCylinderD[- 1/2 -(a), - z]- ParabolicCylinderD[- 1/2 -(a), z])	Failure	Failure	Failed [6 / 21] Result: .3997621251-.6252084121*I Test Values: {a = 3/2, z = -1/2+1/2*I*3^(1/2)} Result: .9306149059+.2046923958*I Test Values: {a = 3/2, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [6 / 21] Result: Complex[0.3997621252402044, -0.6252084117529283] Test Values: {Rule[a, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[0.9306149056064967, 0.20469239560568858] Test Values: {Rule[a, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data
13.18.E14	${\displaystyle{\displaystyle M_{\frac{1}{4}+n,-\frac{1}{4}}\left(z^{2}\right)=(-1)^{n}\frac{n!}{(2n)!}e^{-\frac{1}{2}z^{2}}\sqrt{z}H_{2n}\left(z\right)}}$ \WhittakerconfhyperM{\frac{1}{4}+n}{-\frac{1}{4}}@{z^{2}} = (-1)^{n}\frac{n!}{(2n)!}e^{-\frac{1}{2}z^{2}}\sqrt{z}\HermitepolyH{2n}@{z}		WhittakerM((1)/(4)+ n, -(1)/(4), (z)^(2)) = (- 1)^(n)*(factorial(n))/(factorial(2*n))*exp(-(1)/(2)*(z)^(2))*sqrt(z)*HermiteH(2*n, z)	WhittakerM[Divide[1,4]+ n, -Divide[1,4], (z)^(2)] == (- 1)^(n)*Divide[(n)!,(2*n)!]*Exp[-Divide[1,2]*(z)^(2)]*Sqrt[z]*HermiteH[2*n, z]	Failure	Failure	Failed [6 / 21] Result: 4.741276300-.776142297*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 1} Result: 9.155588595+2.115036937*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 2} ... skip entries to safe data	Failed [6 / 21] Result: Complex[4.741276296912009, -0.7761422976118018] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[9.15558858680754, 2.115036935310196] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.18.E15	${\displaystyle{\displaystyle M_{\frac{3}{4}+n,\frac{1}{4}}\left(z^{2}\right)=(-1)^{n}\frac{n!}{(2n+1)!}\frac{e^{-\frac{1}{2}z^{2}}\sqrt{z}}{2}H_{2n+1}\left(z\right)}}$ \WhittakerconfhyperM{\frac{3}{4}+n}{\frac{1}{4}}@{z^{2}} = (-1)^{n}\frac{n!}{(2n+1)!}\frac{e^{-\frac{1}{2}z^{2}}\sqrt{z}}{2}\HermitepolyH{2n+1}@{z}		WhittakerM((3)/(4)+ n, (1)/(4), (z)^(2)) = (- 1)^(n)*(factorial(n))/(factorial(2*n + 1))*(exp(-(1)/(2)*(z)^(2))*sqrt(z))/(2)*HermiteH(2*n + 1, z)	WhittakerM[Divide[3,4]+ n, Divide[1,4], (z)^(2)] == (- 1)^(n)*Divide[(n)!,(2*n + 1)!]*Divide[Exp[-Divide[1,2]*(z)^(2)]*Sqrt[z],2]*HermiteH[2*n + 1, z]	Failure	Failure	Failed [6 / 21] Result: 2.634248102+.148339259*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 1} Result: 3.481689250+1.400565410*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 2} ... skip entries to safe data	Failed [6 / 21] Result: Complex[2.6342480998741933, 0.14833925882834587] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[3.4816892469231746, 1.4005654089276338] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.18.E16	${\displaystyle{\displaystyle W_{\frac{1}{4}+\frac{1}{2}n,\frac{1}{4}}\left(z^{2}\right)=2^{-n}e^{-\frac{1}{2}z^{2}}\sqrt{z}H_{n}\left(z\right)}}$ \WhittakerconfhyperW{\frac{1}{4}+\frac{1}{2}n}{\frac{1}{4}}@{z^{2}} = 2^{-n}e^{-\frac{1}{2}z^{2}}\sqrt{z}\HermitepolyH{n}@{z}		WhittakerW((1)/(4)+(1)/(2)*n, (1)/(4), (z)^(2)) = (2)^(- n)* exp(-(1)/(2)*(z)^(2))*sqrt(z)*HermiteH(n, z)	WhittakerW[Divide[1,4]+Divide[1,2]*n, Divide[1,4], (z)^(2)] == (2)^(- n)* Exp[-Divide[1,2]*(z)^(2)]*Sqrt[z]*HermiteH[n, z]	Failure	Failure	Failed [6 / 21] Result: 1.704303716-.6267307130*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 1} Result: -2.370638149+.3880711488*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 2} ... skip entries to safe data	Failed [6 / 21] Result: Complex[1.7043037156649337, -0.6267307126437623] Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[-2.370638148456005, 0.388071148805901] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.18.E17	${\displaystyle{\displaystyle W_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}\alpha}\left(z\right)=(-1)^{n}{\left(\alpha+1\right)_{n}}M_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}\alpha}\left(z\right)}}$ \WhittakerconfhyperW{\frac{1}{2}\alpha+\frac{1}{2}+n}{\frac{1}{2}\alpha}@{z} = (-1)^{n}\Pochhammersym{\alpha+1}{n}\WhittakerconfhyperM{\frac{1}{2}\alpha+\frac{1}{2}+n}{\frac{1}{2}\alpha}@{z}		WhittakerW((1)/(2)*alpha +(1)/(2)+ n, (1)/(2)*alpha, z) = (- 1)^(n)* pochhammer(alpha + 1, n)*WhittakerM((1)/(2)*alpha +(1)/(2)+ n, (1)/(2)*alpha, z)	WhittakerW[Divide[1,2]*\[Alpha]+Divide[1,2]+ n, Divide[1,2]*\[Alpha], z] == (- 1)^(n)* Pochhammer[\[Alpha]+ 1, n]*WhittakerM[Divide[1,2]*\[Alpha]+Divide[1,2]+ n, Divide[1,2]*\[Alpha], z]	Failure	Failure	Successful [Tested: 63]	Successful [Tested: 63]
13.18.E17	${\displaystyle{\displaystyle(-1)^{n}{\left(\alpha+1\right)_{n}}M_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}\alpha}\left(z\right)=(-1)^{n}n!e^{-\frac{1}{2}z}z^{\frac{1}{2}\alpha+\frac{1}{2}}L^{(\alpha)}_{n}\left(z\right)}}$ (-1)^{n}\Pochhammersym{\alpha+1}{n}\WhittakerconfhyperM{\frac{1}{2}\alpha+\frac{1}{2}+n}{\frac{1}{2}\alpha}@{z} = (-1)^{n}n!e^{-\frac{1}{2}z}z^{\frac{1}{2}\alpha+\frac{1}{2}}\LaguerrepolyL[\alpha]{n}@{z}		(- 1)^(n)* pochhammer(alpha + 1, n)*WhittakerM((1)/(2)*alpha +(1)/(2)+ n, (1)/(2)*alpha, z) = (- 1)^(n)* factorial(n)*exp(-(1)/(2)*z)*(z)^((1)/(2)*alpha +(1)/(2))* LaguerreL(n, alpha, z)	(- 1)^(n)* Pochhammer[\[Alpha]+ 1, n]*WhittakerM[Divide[1,2]*\[Alpha]+Divide[1,2]+ n, Divide[1,2]*\[Alpha], z] == (- 1)^(n)* (n)!*Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*\[Alpha]+Divide[1,2])* LaguerreL[n, \[Alpha], z]	Missing Macro Error	Successful	Skip - symbolical successful subtest	Successful [Tested: 63]
13.20.E10	${\displaystyle{\displaystyle\zeta=+\sqrt{\frac{x}{\mu}-2-2\ln\left(\frac{x}{2\mu}\right)}}}$ \zeta = +\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}		zeta = +sqrt((x)/(mu)- 2 - 2*ln((x)/(2*mu)))	\[Zeta] == +Sqrt[Divide[x,\[Mu]]- 2 - 2*Log[Divide[x,2*\[Mu]]]]	Failure	Failure	Failed [300 / 300] Result: .5521389640+.265842778e-1*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: -.8138864400+.3926096818*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.552138964202831, 0.026584277433671977] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.016922323883714174, -1.2016497569691986] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.20.E10	${\displaystyle{\displaystyle\zeta=-\sqrt{\frac{x}{\mu}-2-2\ln\left(\frac{x}{2\mu}\right)}}}$ \zeta = -\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}		zeta = -sqrt((x)/(mu)- 2 - 2*ln((x)/(2*mu)))	\[Zeta] == -Sqrt[Divide[x,\[Mu]]- 2 - 2*Log[Divide[x,2*\[Mu]]]]	Failure	Failure	Failed [300 / 300] Result: 1.179911844+.9734157222*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: -.1861135600+1.339441126*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.1799118433660465, 0.9734157225663279] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.7151284836851632, 2.2016497569691986] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.21.E5	${\displaystyle{\displaystyle 2\sqrt{\zeta}=\sqrt{x+x^{2}}+\ln\left(\sqrt{x}+\sqrt{1+x}\right)}}$ 2\sqrt{\zeta} = \sqrt{x+x^{2}}+\ln@{\sqrt{x}+\sqrt{1+x}}		2*sqrt(zeta) = sqrt(x + (x)^(2))+ ln(sqrt(x)+sqrt(1 + x))	2*Sqrt[\[Zeta]] == Sqrt[x + (x)^(2)]+ Log[Sqrt[x]+Sqrt[1 + x]]	Failure	Failure	Failed [30 / 30] Result: -1.036358555+.5176380902*I Test Values: {x = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: -1.968210208+1.732050808*I Test Values: {x = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [30 / 30] Result: Complex[-1.0363585549733523, 0.5176380902050415] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.9682102075514887, 1.7320508075688772] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.23.E1	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\mu+\nu+\tfrac{1}{2}\right)}{\left(z+\frac{1}{2}\right)^{\mu+\nu+\frac{1}{2}}}\*{{}_{2}F_{1}}\left({\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}+\mu+\nu\atop 1+2\mu};\frac{1}{z+\frac{1}{2}}\right)}}$ \int_{0}^{\infty}e^{-zt}t^{\nu-1}\WhittakerconfhyperM{\kappa}{\mu}@{t}\diff{t} = \frac{\EulerGamma@{\mu+\nu+\tfrac{1}{2}}}{\left(z+\frac{1}{2}\right)^{\mu+\nu+\frac{1}{2}}}\*\genhyperF{2}{1}@@{\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}+\mu+\nu}{1+2\mu}{\frac{1}{z+\frac{1}{2}}}	${\displaystyle{\displaystyle\Re\mu+\nu+\tfrac{1}{2}>0,\Re z>\tfrac{1}{2},\Re(\mu+\nu+\tfrac{1}{2})>0}}$	int(exp(- z*t)*(t)^(nu - 1)* WhittakerM(kappa, mu, t), t = 0..infinity) = (GAMMA(mu + nu +(1)/(2)))/((z +(1)/(2))^(mu + nu +(1)/(2)))* hypergeom([(1)/(2)+ mu - kappa ,(1)/(2)+ mu + nu], [1 + 2*mu], (1)/(z +(1)/(2)))	Integrate[Exp[- z*t]*(t)^(\[Nu]- 1)* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Mu]+ \[Nu]+Divide[1,2]],(z +Divide[1,2])^(\[Mu]+ \[Nu]+Divide[1,2])]* HypergeometricPFQ[{Divide[1,2]+ \[Mu]- \[Kappa],Divide[1,2]+ \[Mu]+ \[Nu]}, {1 + 2*\[Mu]}, Divide[1,z +Divide[1,2]]]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.23.E2	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\mu-\frac{1}{2}}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\Gamma\left(2\mu+1\right)\left(z+\tfrac{1}{2}\right)^{-\kappa-\mu-\frac{1}{2}}\*\left(z-\tfrac{1}{2}\right)^{\kappa-\mu-\frac{1}{2}}}}$ \int_{0}^{\infty}e^{-zt}t^{\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{t}\diff{t} = \EulerGamma@{2\mu+1}\left(z+\tfrac{1}{2}\right)^{-\kappa-\mu-\frac{1}{2}}\*\left(z-\tfrac{1}{2}\right)^{\kappa-\mu-\frac{1}{2}}	${\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2},\Re z>\tfrac{1}{2},\Re(2\mu+1)>0}}$	int(exp(- z*t)*(t)^(mu -(1)/(2))* WhittakerM(kappa, mu, t), t = 0..infinity) = GAMMA(2*mu + 1)*(z +(1)/(2))^(- kappa - mu -(1)/(2))*(z -(1)/(2))^(kappa - mu -(1)/(2))	Integrate[Exp[- z*t]*(t)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}, GenerateConditions->None] == Gamma[2*\[Mu]+ 1]*(z +Divide[1,2])^(- \[Kappa]- \[Mu]-Divide[1,2])*(z -Divide[1,2])^(\[Kappa]- \[Mu]-Divide[1,2])	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.23.E3	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\mu+\nu+\frac{1}{2}\right)\Gamma\left(\kappa-\nu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)\Gamma\left(\frac{1}{2}+\mu-\nu\right)}}}$ \frac{1}{\EulerGamma@{1+2\mu}}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\nu-1}\WhittakerconfhyperM{\kappa}{\mu}@{t}\diff{t} = \frac{\EulerGamma@{\mu+\nu+\frac{1}{2}}\EulerGamma@{\kappa-\nu}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}\EulerGamma@{\frac{1}{2}+\mu-\nu}}	${\displaystyle{\displaystyle-\tfrac{1}{2}-\Re\mu<\Re\nu,\Re\nu<\Re\kappa,\Re(1+2\mu)>0,\Re(\mu+\nu+\frac{1}{2})>0,\Re(\kappa-\nu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0,\Re(\frac{1}{2}+\mu-\nu)>0}}$	(1)/(GAMMA(1 + 2*mu))*int(exp(-(1)/(2)*t)*(t)^(nu - 1)* WhittakerM(kappa, mu, t), t = 0..infinity) = (GAMMA(mu + nu +(1)/(2))*GAMMA(kappa - nu))/(GAMMA((1)/(2)+ mu + kappa)*GAMMA((1)/(2)+ mu - nu))	Divide[1,Gamma[1 + 2*\[Mu]]]*Integrate[Exp[-Divide[1,2]*t]*(t)^(\[Nu]- 1)* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Mu]+ \[Nu]+Divide[1,2]]*Gamma[\[Kappa]- \[Nu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]- \[Nu]]]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.23.E4	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\nu-1}W_{\kappa,\mu}\left(t\right)\mathrm{d}t=\Gamma\left(\tfrac{1}{2}+\mu+\nu\right)\Gamma\left(\tfrac{1}{2}-\mu+\nu\right)\*{{}_{2}{\mathbf{F}}_{1}}\left({\tfrac{1}{2}-\mu+\nu,\tfrac{1}{2}+\mu+\nu\atop\nu-\kappa+1};\tfrac{1}{2}-z\right)}}$ \int_{0}^{\infty}e^{-zt}t^{\nu-1}\WhittakerconfhyperW{\kappa}{\mu}@{t}\diff{t} = \EulerGamma@{\tfrac{1}{2}+\mu+\nu}\EulerGamma@{\tfrac{1}{2}-\mu+\nu}\*\genhyperOlverF{2}{1}@@{\tfrac{1}{2}-\mu+\nu,\tfrac{1}{2}+\mu+\nu}{\nu-\kappa+1}{\tfrac{1}{2}-z}	${\displaystyle{\displaystyle\Re\left(\nu+\tfrac{1}{2}\right)>|\Re\mu|,\Re z>-\tfrac{1}{2},\Re(\tfrac{1}{2}+\mu+\nu)>0,\Re(\tfrac{1}{2}-\mu+\nu)>0}}$	int(exp(- z*t)*(t)^(nu - 1)* WhittakerW(kappa, mu, t), t = 0..infinity) = GAMMA((1)/(2)+ mu + nu)*GAMMA((1)/(2)- mu + nu)* hypergeom([(1)/(2)- mu + nu ,(1)/(2)+ mu + nu], [nu - kappa + 1], (1)/(2)- z)	Integrate[Exp[- z*t]*(t)^(\[Nu]- 1)* WhittakerW[\[Kappa], \[Mu], t], {t, 0, Infinity}, GenerateConditions->None] == Gamma[Divide[1,2]+ \[Mu]+ \[Nu]]*Gamma[Divide[1,2]- \[Mu]+ \[Nu]]* HypergeometricPFQRegularized[{Divide[1,2]- \[Mu]+ \[Nu],Divide[1,2]+ \[Mu]+ \[Nu]}, {\[Nu]- \[Kappa]+ 1}, Divide[1,2]- z]	Failure	Aborted	Failed [276 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = 1/2} Result: .2394973555+.5504747838e-1*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2-1/2*I*3^(1/2), z = 1/2*3^(1/2)+1/2*I} ... skip entries to safe data	Skipped - Because timed out
13.23.E5	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{\frac{1}{2}t}t^{\nu-1}W_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac{\Gamma\left(\frac{1}{2}+\mu+\nu\right)\Gamma\left(\frac{1}{2}-\mu+\nu\right)\Gamma\left(-\kappa-\nu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}}}$ \int_{0}^{\infty}e^{\frac{1}{2}t}t^{\nu-1}\WhittakerconfhyperW{\kappa}{\mu}@{t}\diff{t} = \frac{\EulerGamma@{\frac{1}{2}+\mu+\nu}\EulerGamma@{\frac{1}{2}-\mu+\nu}\EulerGamma@{-\kappa-\nu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}	${\displaystyle{\displaystyle|\Re\mu|-\tfrac{1}{2}<\Re\nu,\Re\nu<-\Re\kappa,\Re(\frac{1}{2}+\mu+\nu)>0,\Re(\frac{1}{2}-\mu+\nu)>0,\Re(-\kappa-\nu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	int(exp((1)/(2)*t)*(t)^(nu - 1)* WhittakerW(kappa, mu, t), t = 0..infinity) = (GAMMA((1)/(2)+ mu + nu)*GAMMA((1)/(2)- mu + nu)*GAMMA(- kappa - nu))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))	Integrate[Exp[Divide[1,2]*t]*(t)^(\[Nu]- 1)* WhittakerW[\[Kappa], \[Mu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]+ \[Mu]+ \[Nu]]*Gamma[Divide[1,2]- \[Mu]+ \[Nu]]*Gamma[- \[Kappa]- \[Nu]],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]	Failure	Aborted	Manual Skip!	Successful [Tested: 56]
13.23.E6	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}M_{\kappa,\mu}\left(t^{-1}\right)\mathrm{d}t=\frac{z^{-\kappa-\frac{1}{2}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}I_{2\mu}\left(2\sqrt{z}\right)}}$ \frac{1}{\EulerGamma@{1+2\mu}2\pi\iunit}\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}\WhittakerconfhyperM{\kappa}{\mu}@{t^{-1}}\diff{t} = \frac{z^{-\kappa-\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\modBesselI{2\mu}@{2\sqrt{z}}	${\displaystyle{\displaystyle\Re z>0,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re((2\mu)+k+1)>0}}$	(1)/(GAMMA(1 + 2*mu)*2*Pi*I)*int(exp(z*t +(1)/(2)*(t)^(- 1))*(t)^(kappa)* WhittakerM(kappa, mu, (t)^(- 1)), t = - infinity..(0 +)) = ((z)^(- kappa -(1)/(2)))/(GAMMA((1)/(2)+ mu - kappa))*BesselI(2*mu, 2*sqrt(z))	Divide[1,Gamma[1 + 2*\[Mu]]*2*Pi*I]*Integrate[Exp[z*t +Divide[1,2]*(t)^(- 1)]*(t)^\[Kappa]* WhittakerM[\[Kappa], \[Mu], (t)^(- 1)], {t, - Infinity, (0 +)}, GenerateConditions->None] == Divide[(z)^(- \[Kappa]-Divide[1,2]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*BesselI[2*\[Mu], 2*Sqrt[z]]	Error	Failure	-	Error
13.23.E7	${\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}W_{\kappa,\mu}\left(t^{-1}\right)\mathrm{d}t=\frac{2z^{-\kappa-\frac{1}{2}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}K_{2\mu}\left(2\sqrt{z}\right)}}$ \frac{1}{2\pi\iunit}\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}\WhittakerconfhyperW{\kappa}{\mu}@{t^{-1}}\diff{t} = \frac{2z^{-\kappa-\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\modBesselK{2\mu}@{2\sqrt{z}}	${\displaystyle{\displaystyle\Re z>0,\Re(\frac{1}{2}+\mu-\kappa)>0,\Re(\frac{1}{2}-\mu-\kappa)>0}}$	(1)/(2*Pi*I)*int(exp(z*t +(1)/(2)*(t)^(- 1))*(t)^(kappa)* WhittakerW(kappa, mu, (t)^(- 1)), t = - infinity..(0 +)) = (2*(z)^(- kappa -(1)/(2)))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))*BesselK(2*mu, 2*sqrt(z))	Divide[1,2*Pi*I]*Integrate[Exp[z*t +Divide[1,2]*(t)^(- 1)]*(t)^\[Kappa]* WhittakerW[\[Kappa], \[Mu], (t)^(- 1)], {t, - Infinity, (0 +)}, GenerateConditions->None] == Divide[2*(z)^(- \[Kappa]-Divide[1,2]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*BesselK[2*\[Mu], 2*Sqrt[z]]	Error	Failure	-	Error
13.23.E8	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{\infty}\cos\left(2xt\right)e^{-\frac{1}{2}t^{2}}t^{-2\mu-1}M_{\kappa,\mu}\left(t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}e^{-\frac{1}{2}x^{2}}x^{\mu+\kappa-1}}{2\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}W_{\frac{1}{2}\kappa-\frac{3}{2}\mu,\frac{1}{2}\kappa+\frac{1}{2}\mu}\left(x^{2}\right)}}$ \frac{1}{\EulerGamma@{1+2\mu}}\int_{0}^{\infty}\cos@{2xt}e^{-\frac{1}{2}t^{2}}t^{-2\mu-1}\WhittakerconfhyperM{\kappa}{\mu}@{t^{2}}\diff{t} = \frac{\sqrt{\pi}e^{-\frac{1}{2}x^{2}}x^{\mu+\kappa-1}}{2\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\WhittakerconfhyperW{\frac{1}{2}\kappa-\frac{3}{2}\mu}{\frac{1}{2}\kappa+\frac{1}{2}\mu}@{x^{2}}	${\displaystyle{\displaystyle\Re\left(\kappa+\mu\right)>-\tfrac{1}{2},\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0}}$	(1)/(GAMMA(1 + 2*mu))*int(cos(2*x*t)*exp(-(1)/(2)*(t)^(2))*(t)^(- 2*mu - 1)* WhittakerM(kappa, mu, (t)^(2)), t = 0..infinity) = (sqrt(Pi)*exp(-(1)/(2)*(x)^(2))*(x)^(mu + kappa - 1))/(2*GAMMA((1)/(2)+ mu + kappa))*WhittakerW((1)/(2)*kappa -(3)/(2)*mu, (1)/(2)*kappa +(1)/(2)*mu, (x)^(2))	Divide[1,Gamma[1 + 2*\[Mu]]]*Integrate[Cos[2*x*t]*Exp[-Divide[1,2]*(t)^(2)]*(t)^(- 2*\[Mu]- 1)* WhittakerM[\[Kappa], \[Mu], (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi]*Exp[-Divide[1,2]*(x)^(2)]*(x)^(\[Mu]+ \[Kappa]- 1),2*Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*WhittakerW[Divide[1,2]*\[Kappa]-Divide[3,2]*\[Mu], Divide[1,2]*\[Kappa]+Divide[1,2]*\[Mu], (x)^(2)]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.23.E9	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\mu-\frac{1}{2}(\nu+1)}M_{\kappa,\mu}\left(t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{\Gamma\left(1+2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu+\kappa+\nu\right)}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa-\mu-\frac{3}{2})}\*M_{\frac{1}{2}(\kappa+3\mu-\nu+\frac{1}{2}),\frac{1}{2}(\kappa-\mu+\nu-\frac{1}{2})}\left(x\right)}}$ \int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\mu-\frac{1}{2}(\nu+1)}\WhittakerconfhyperM{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa+\nu}}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa-\mu-\frac{3}{2})}\*\WhittakerconfhyperM{\frac{1}{2}(\kappa+3\mu-\nu+\frac{1}{2})}{\frac{1}{2}(\kappa-\mu+\nu-\frac{1}{2})}@{x}	${\displaystyle{\displaystyle x>0,-\tfrac{1}{2}<\Re\mu,\Re\mu<\Re\left(\kappa+\tfrac{1}{2}\nu\right)+\tfrac{3}{4},\Re(\nu+k+1)>0,\Re(1+2\mu)>0,\Re(\frac{1}{2}-\mu+\kappa+\nu)>0}}$	int(exp(-(1)/(2)*t)*(t)^(mu -(1)/(2)*(nu + 1))* WhittakerM(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity) = (GAMMA(1 + 2*mu))/(GAMMA((1)/(2)- mu + kappa + nu))* exp(-(1)/(2)*x)*(x)^((1)/(2)*(kappa - mu -(3)/(2)))* WhittakerM((1)/(2)*(kappa + 3*mu - nu +(1)/(2)), (1)/(2)*(kappa - mu + nu -(1)/(2)), x)	Integrate[Exp[-Divide[1,2]*t]*(t)^(\[Mu]-Divide[1,2]*(\[Nu]+ 1))* WhittakerM[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]+ \[Nu]]]* Exp[-Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Kappa]- \[Mu]-Divide[3,2]))* WhittakerM[Divide[1,2]*(\[Kappa]+ 3*\[Mu]- \[Nu]+Divide[1,2]), Divide[1,2]*(\[Kappa]- \[Mu]+ \[Nu]-Divide[1,2]), x]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.23.E10	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}M_{\kappa,\mu}\left(t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa+\mu-\frac{3}{2})}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*W_{\frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2}),\frac{1}{2}(\kappa+\mu-\nu-\frac{1}{2})}\left(x\right)}}$ \frac{1}{\EulerGamma@{1+2\mu}}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}\WhittakerconfhyperM{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa+\mu-\frac{3}{2})}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\*\WhittakerconfhyperW{\frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2})}{\frac{1}{2}(\kappa+\mu-\nu-\frac{1}{2})}@{x}	${\displaystyle{\displaystyle x>0,-1<\Re\nu,\Re\nu<2\Re\left(\mu+\kappa\right)+\tfrac{1}{2},\Re(\nu+k+1)>0,\Re(1+2\mu)>0,\Re(\frac{1}{2}+\mu+\kappa)>0}}$	(1)/(GAMMA(1 + 2*mu))*int(exp(-(1)/(2)*t)*(t)^((1)/(2)*(nu - 1)- mu)* WhittakerM(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity) = (exp(-(1)/(2)*x)*(x)^((1)/(2)*(kappa + mu -(3)/(2))))/(GAMMA((1)/(2)+ mu + kappa))* WhittakerW((1)/(2)*(kappa - 3*mu + nu +(1)/(2)), (1)/(2)*(kappa + mu - nu -(1)/(2)), x)	Divide[1,Gamma[1 + 2*\[Mu]]]*Integrate[Exp[-Divide[1,2]*t]*(t)^(Divide[1,2]*(\[Nu]- 1)- \[Mu])* WhittakerM[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}, GenerateConditions->None] == Divide[Exp[-Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Kappa]+ \[Mu]-Divide[3,2])),Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]* WhittakerW[Divide[1,2]*(\[Kappa]- 3*\[Mu]+ \[Nu]+Divide[1,2]), Divide[1,2]*(\[Kappa]+ \[Mu]- \[Nu]-Divide[1,2]), x]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
13.23.E11	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}W_{\kappa,\mu}\left(t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{\Gamma\left(\nu-2\mu+1\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*e^{\frac{1}{2}x}x^{\frac{1}{2}(\mu-\kappa-\frac{3}{2})}\*W_{\frac{1}{2}(\kappa+3\mu-\nu-\frac{1}{2}),\frac{1}{2}(\kappa-\mu+\nu+\frac{1}{2})}\left(x\right)}}$ \int_{0}^{\infty}e^{\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}\WhittakerconfhyperW{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{\nu-2\mu+1}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*e^{\frac{1}{2}x}x^{\frac{1}{2}(\mu-\kappa-\frac{3}{2})}\*\WhittakerconfhyperW{\frac{1}{2}(\kappa+3\mu-\nu-\frac{1}{2})}{\frac{1}{2}(\kappa-\mu+\nu+\frac{1}{2})}@{x}	${\displaystyle{\displaystyle x>0,\max(2\Re\mu-1<\Re\nu,-1)<\Re\nu,\Re\nu<2\Re\mu-\kappa+\tfrac{3}{2},\Re(\nu+k+1)>0,\Re(\nu-2\mu+1)>0,\Re(\frac{1}{2}+\mu-\kappa)>0}}$	int(exp((1)/(2)*t)*(t)^((1)/(2)*(nu - 1)- mu)* WhittakerW(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity) = (GAMMA(nu - 2*mu + 1))/(GAMMA((1)/(2)+ mu - kappa))* exp((1)/(2)*x)*(x)^((1)/(2)*(mu - kappa -(3)/(2)))* WhittakerW((1)/(2)*(kappa + 3*mu - nu -(1)/(2)), (1)/(2)*(kappa - mu + nu +(1)/(2)), x)	Integrate[Exp[Divide[1,2]*t]*(t)^(Divide[1,2]*(\[Nu]- 1)- \[Mu])* WhittakerW[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Nu]- 2*\[Mu]+ 1],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Exp[Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Mu]- \[Kappa]-Divide[3,2]))* WhittakerW[Divide[1,2]*(\[Kappa]+ 3*\[Mu]- \[Nu]-Divide[1,2]), Divide[1,2]*(\[Kappa]- \[Mu]+ \[Nu]+Divide[1,2]), x]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
13.23.E12	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}W_{\kappa,\mu}\left(t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{\Gamma\left(\nu-2\mu+1\right)}{\Gamma\left(\frac{3}{2}-\mu-\kappa+\nu\right)}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\mu+\kappa-\frac{3}{2})}\*M_{\frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2}),\frac{1}{2}(\nu-\mu-\kappa+\frac{1}{2})}\left(x\right)}}$ \int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}\WhittakerconfhyperW{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{\nu-2\mu+1}}{\EulerGamma@{\frac{3}{2}-\mu-\kappa+\nu}}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\mu+\kappa-\frac{3}{2})}\*\WhittakerconfhyperM{\frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2})}{\frac{1}{2}(\nu-\mu-\kappa+\frac{1}{2})}@{x}	${\displaystyle{\displaystyle x>0,\max(2\Re\mu-1<\Re\nu,-1)<\Re\nu,\Re(\nu+k+1)>0,\Re(\nu-2\mu+1)>0,\Re(\frac{3}{2}-\mu-\kappa+\nu)>0}}$	int(exp(-(1)/(2)*t)*(t)^((1)/(2)*(nu - 1)- mu)* WhittakerW(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity) = (GAMMA(nu - 2*mu + 1))/(GAMMA((3)/(2)- mu - kappa + nu))* exp(-(1)/(2)*x)*(x)^((1)/(2)*(mu + kappa -(3)/(2)))* WhittakerM((1)/(2)*(kappa - 3*mu + nu +(1)/(2)), (1)/(2)*(nu - mu - kappa +(1)/(2)), x)	Integrate[Exp[-Divide[1,2]*t]*(t)^(Divide[1,2]*(\[Nu]- 1)- \[Mu])* WhittakerW[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Nu]- 2*\[Mu]+ 1],Gamma[Divide[3,2]- \[Mu]- \[Kappa]+ \[Nu]]]* Exp[-Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Mu]+ \[Kappa]-Divide[3,2]))* WhittakerM[Divide[1,2]*(\[Kappa]- 3*\[Mu]+ \[Nu]+Divide[1,2]), Divide[1,2]*(\[Nu]- \[Mu]- \[Kappa]+Divide[1,2]), x]	Failure	Aborted	Manual Skip!	Skipped - Because timed out
13.24.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\Gamma\left(\kappa+\mu\right)2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\*\sum_{s=0}^{\infty}(-1)^{s}\frac{{\left(2\kappa+2\mu\right)_{s}}{\left(2\kappa\right)_{s}}}{{\left(1+2\mu\right)_{s}}s!}\*\left(\kappa+\mu+s\right)I_{\kappa+\mu+s}\left(\tfrac{1}{2}z\right)}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z} = \EulerGamma@{\kappa+\mu}2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\*\sum_{s=0}^{\infty}(-1)^{s}\frac{\Pochhammersym{2\kappa+2\mu}{s}\Pochhammersym{2\kappa}{s}}{\Pochhammersym{1+2\mu}{s}s!}\*\left(\kappa+\mu+s\right)\modBesselI{\kappa+\mu+s}@{\tfrac{1}{2}z}	${\displaystyle{\displaystyle\Re(\kappa+\mu)>0,\Re((\kappa+\mu+s)+k+1)>0}}$	WhittakerM(kappa, mu, z) = GAMMA(kappa + mu)*(2)^(2*kappa + 2*mu)* (z)^((1)/(2)- kappa)* sum((- 1)^(s)*(pochhammer(2*kappa + 2*mu, s)*pochhammer(2*kappa, s))/(pochhammer(1 + 2*mu, s)*factorial(s))*(kappa + mu + s)*BesselI(kappa + mu + s, (1)/(2)*z), s = 0..infinity)	WhittakerM[\[Kappa], \[Mu], z] == Gamma[\[Kappa]+ \[Mu]]*(2)^(2*\[Kappa]+ 2*\[Mu])* (z)^(Divide[1,2]- \[Kappa])* Sum[(- 1)^(s)*Divide[Pochhammer[2*\[Kappa]+ 2*\[Mu], s]*Pochhammer[2*\[Kappa], s],Pochhammer[1 + 2*\[Mu], s]*(s)!]*(\[Kappa]+ \[Mu]+ s)*BesselI[\[Kappa]+ \[Mu]+ s, Divide[1,2]*z], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Manual Skip!	Skipped - Because timed out
13.24.E2	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=2^{2\mu}z^{\mu+\frac{1}{2}}\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(2\sqrt{\kappa z}\right)^{-2\mu-s}J_{2\mu+s}\left(2\sqrt{\kappa z}\right)}}$ \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = 2^{2\mu}z^{\mu+\frac{1}{2}}\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(2\sqrt{\kappa z}\right)^{-2\mu-s}\BesselJ{2\mu+s}@{2\sqrt{\kappa z}}	${\displaystyle{\displaystyle\Re((2\mu+s)+k+1)>0,\Re(1+2\mu)>0}}$	(1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z) = (2)^(2*mu)* (z)^(mu +(1)/(2))* sum((p[s])^(mu)(z)*(2*sqrt(kappa*z))^(- 2*mu - s)* BesselJ(2*mu + s, 2*sqrt(kappa*z)), s = 0..infinity)	Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z] == (2)^(2*\[Mu])* (z)^(\[Mu]+Divide[1,2])* Sum[(Subscript[p, s])^(\[Mu])[z]*(2*Sqrt[\[Kappa]*z])^(- 2*\[Mu]- s)* BesselJ[2*\[Mu]+ s, 2*Sqrt[\[Kappa]*z]], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
13.24.E3	${\displaystyle{\displaystyle\exp\left(-\tfrac{1}{2}z\left(\coth t-\frac{1}{t}\right)\right)\left(\frac{t}{\sinh t}\right)^{1-2\mu}=\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(-\frac{t}{z}\right)^{s}}}$ \exp@{-\tfrac{1}{2}z\left(\coth@@{t}-\frac{1}{t}\right)}\left(\frac{t}{\sinh@@{t}}\right)^{1-2\mu} = \sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(-\frac{t}{z}\right)^{s}		exp(-(1)/(2)*z*(coth(t)-(1)/(t)))*((t)/(sinh(t)))^(1 - 2*mu) = sum((p[s])^(mu)(z)*(-(t)/(z))^(s), s = 0..infinity)	Exp[-Divide[1,2]*z*(Coth[t]-Divide[1,t])]*(Divide[t,Sinh[t]])^(1 - 2*\[Mu]) == Sum[(Subscript[p, s])^(\[Mu])[z]*(-Divide[t,z])^(s), {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Plus[Complex[1.4000146541353637, 0.6933735030866136], Times[-1.0, NSum[Times[Power[Complex[1.299038105676658, -0.7499999999999999], s], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], p] Test Values: {s, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, s], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[1.4000146541353637, 0.6933735030866136], Times[-1.0, NSum[Times[Power[Complex[1.299038105676658, -0.7499999999999999], s], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], p] Test Values: {s, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, s], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.25.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)M_{\kappa,-\mu-1}\left(z\right)+\frac{(\frac{1}{2}+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}M_{\kappa,\mu+1}\left(z\right)M_{\kappa,-\mu}\left(z\right)=1}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z}\WhittakerconfhyperM{\kappa}{-\mu-1}@{z}+\frac{(\frac{1}{2}+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}\WhittakerconfhyperM{\kappa}{\mu+1}@{z}\WhittakerconfhyperM{\kappa}{-\mu}@{z} = 1		WhittakerM(kappa, mu, z)*WhittakerM(kappa, - mu - 1, z)+(((1)/(2)+ mu + kappa)*((1)/(2)+ mu - kappa))/(4*mu*(1 + mu)*(1 + 2*mu)^(2))*WhittakerM(kappa, mu + 1, z)*WhittakerM(kappa, - mu, z) = 1	WhittakerM[\[Kappa], \[Mu], z]*WhittakerM[\[Kappa], - \[Mu]- 1, z]+Divide[(Divide[1,2]+ \[Mu]+ \[Kappa])*(Divide[1,2]+ \[Mu]- \[Kappa]),4*\[Mu]*(1 + \[Mu])*(1 + 2*\[Mu])^(2)]*WhittakerM[\[Kappa], \[Mu]+ 1, z]*WhittakerM[\[Kappa], - \[Mu], z] == 1	Failure	Failure	Failed [168 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = -3/2, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = -3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [162 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, 1.5]} ... skip entries to safe data
13.28#Ex1	${\displaystyle{\displaystyle f_{1}(\xi)=\xi^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(1)}(2\mathrm{i}k\xi)}}$ f_{1}(\xi) = \xi^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(1)}(2\iunit k\xi)		f[1](xi) = (xi)^(-(1)/(2))* (V[kappa ,(1)/(2)*p])^(1)(2*I*k*xi)	Subscript[f, 1][\[Xi]] == \[Xi]^(-Divide[1,2])* (Subscript[V, \[Kappa],Divide[1,2]*p])^(1)[2*I*k*\[Xi]]	Failure	Failure	Failed [300 / 300] Result: 1.914213563-.5481881590*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, k = 1} Result: 3.328427125-1.962401722*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.914213562373095, -0.5481881585886565] Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[3.32842712474619, -1.9624017209617517] Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.28#Ex2	${\displaystyle{\displaystyle f_{2}(\eta)=\eta^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(2)}(-2\mathrm{i}k\eta)}}$ f_{2}(\eta) = \eta^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(2)}(-2\iunit k\eta)		f[2](eta) = (eta)^(-(1)/(2))* (V[kappa ,(1)/(2)*p])^(2)(- 2*I*k*eta)	Subscript[f, 2][\[Eta]] == \[Eta]^(-Divide[1,2])* (Subscript[V, \[Kappa],Divide[1,2]*p])^(2)[- 2*I*k*\[Eta]]	Failure	Failure	Failed [300 / 300] Result: -1.431851653+1.383663495*I Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, k = 1} Result: -3.363703307+1.901301586*I Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.4318516525781364, 1.3836634939894803] Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-3.363703305156273, 1.9013015841945222] Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.29.E1	${\displaystyle{\displaystyle\frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1)=0}}$ \frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0		((x + y*I)^(2)*(n + mu -(1)/(2))*((n + mu +(1)/(2))^(2)- (kappa)^(2)))/((n + mu)*(n + mu +(1)/(2))*(n + mu + 1))*y*(n + 1)+ 16*((n + mu)^(2)-(1)/(2)*kappa*(x + y*I)-(1)/(4))*((x + y*I)^(- n - mu -(1)/(2))* WhittakerM(kappa, n + mu, x + y*I))*; - 16*((n + mu)^(2)-(1)/(4))*y*(n - 1) = 0	Divide[(x + y*I)^(2)*(n + \[Mu]-Divide[1,2])*((n + \[Mu]+Divide[1,2])^(2)- \[Kappa]^(2)),(n + \[Mu])*(n + \[Mu]+Divide[1,2])*(n + \[Mu]+ 1)]*y*(n + 1)+ 16*((n + \[Mu])^(2)-Divide[1,2]*\[Kappa]*(x + y*I)-Divide[1,4])*((x + y*I)^(- n - \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], n + \[Mu], x + y*I])*- 16*((n + \[Mu])^(2)-Divide[1,4])*y*(n - 1) == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
13.29.E3	${\displaystyle{\displaystyle e^{-\frac{1}{2}z}=\sum_{s=0}^{\infty}\frac{{\left(2\mu\right)_{s}}{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(2\mu\right)_{2s}}s!}(-z)^{s}y(s)}}$ e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)		exp(-(1)/(2)*(x + y(I))) = sum((pochhammer(2*mu, s)*pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(2*mu, 2*s)*factorial(s))*(-(x + y(I)))^(s)* y(s), s = 0..infinity)	Exp[-Divide[1,2]*(x + y[I])] == Sum[Divide[Pochhammer[2*\[Mu], s]*Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[2*\[Mu], 2*s]*(s)!]*(-(x + y[I]))^(s)* y[s], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: .505394540e-1+.5994002652*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2} Result: .7100232023-.2722368431*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.0505394539002913, 0.5994002653939074] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.9437946777348876, -0.07485124664222054] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.29.E5	${\displaystyle{\displaystyle(n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2)=0}}$ (n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0		(n + a)*w(n)-(2*(n + a + 1)+ z - b)*w(n + 1)+(n + a - b + 2)*w(n + 2) = 0	(n + a)*w[n]-(2*(n + a + 1)+ z - b)*w[n + 1]+(n + a - b + 2)*w[n + 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
13.29.E6	${\displaystyle{\displaystyle w(n)={\left(a\right)_{n}}U\left(n+a,b,z\right)}}$ w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}		w(n) = pochhammer(a, n)*KummerU(n + a, b, z)	w[n] == Pochhammer[a, n]*HypergeometricU[n + a, b, z]	Failure	Failure	Failed [300 / 300] Result: 3.350777422+.7382256467*I Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1} Result: 1.327538097+1.034245119*I Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[3.3507774204902745, 0.7382256467588033] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.3275380963595516, 1.0342451193960447] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.29.E7	${\displaystyle{\displaystyle z^{-a}=\sum_{s=0}^{\infty}\frac{{\left(a-b+1\right)_{s}}}{s!}w(s)}}$ z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)		(z)^(- a) = sum((pochhammer(a - b + 1, s))/(factorial(s))*w(s), s = 0..infinity)	(z)^(- a) == Sum[Divide[Pochhammer[a - b + 1, s],(s)!]*w[s], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: DirectedInfinity[] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: DirectedInfinity[] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.31.E3	${\displaystyle{\displaystyle z^{a}U\left(a,1+a-b,z\right)=\lim_{n\to\infty}\frac{A_{n}(z)}{B_{n}(z)}}}$ z^{a}\KummerconfhyperU@{a}{1+a-b}{z} = \lim_{n\to\infty}\frac{A_{n}(z)}{B_{n}(z)}		(z)^(a)* KummerU(a, 1 + a - b, z) = limit((sum((pochhammer(- n, s)*pochhammer(n + 1, s)*pochhammer(a, s)*pochhammer(b, s))/(pochhammer(a + 1, s)*pochhammer(b + 1, s)*(factorial(n))^(2))* hypergeom([- n + s , n + 1 + s , 1], [1 + s , a + 1 + s , b + 1 + s], - z), s = 0..n))/(hypergeom([- n , n + 1], [a + 1 , b + 1], - z)), n = infinity)	(z)^(a)* HypergeometricU[a, 1 + a - b, z] == Limit[Divide[Sum[Divide[Pochhammer[- n, s]*Pochhammer[n + 1, s]*Pochhammer[a, s]*Pochhammer[b, s],Pochhammer[a + 1, s]*Pochhammer[b + 1, s]*((n)!)^(2)]* HypergeometricPFQ[{- n + s , n + 1 + s , 1}, {1 + s , a + 1 + s , b + 1 + s}, - z], {s, 0, n}, GenerateConditions->None],HypergeometricPFQ[{- n , n + 1}, {a + 1 , b + 1}, - z]], n -> Infinity, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out