Results of Confluent Hypergeometric Functions

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.2.E1	${\displaystyle{\displaystyle z\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+(b-z% )\frac{\mathrm{d}w}{\mathrm{d}z}-aw=0}}$	`zdiff(w, [z$(2)])+(b - z) diff(w, z)- a*w = 0`	`zD[w, {z, 2}]+(b - z) D[w, z]- a*w = 0`	Failure	Failure	Fail `-0.-3.999999998I <- {a = 2^(1/2)+I2^(1/2), w = 2^(1/2)+I2^(1/2)}` `-3.999999998-0.I <- {a = 2^(1/2)+I2^(1/2), w = 2^(1/2)-I2^(1/2)}` `-0.+3.999999998I <- {a = 2^(1/2)+I2^(1/2), w = -2^(1/2)-I2^(1/2)}` `3.999999998-0.I <- {a = 2^(1/2)+I2^(1/2), w = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[0.0, -4.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `-4.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.0, 4.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `4.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.2.E2	${\displaystyle{\displaystyle M\left(a,b,z\right)=\sum_{s=0}^{\infty}\frac{{% \left(a\right)_{s}}}{{\left(b\right)_{s}}s!}z^{s}}}$	`KummerM(a, b, z)= sum((pochhammer(a, s))/(pochhammer(b, s)factorial(s))(z)^(s), s = 0..infinity)`	`Hypergeometric1F1[a, b, z]= Sum[Divide[Pochhammer[a, s],Pochhammer[b, s](s)!](z)^(s), {s, 0, Infinity}]`	Successful	Successful	-	-
13.2.E3	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}}{\Gamma\left(b+s\right)s!}z^{s}}}$	`KummerM(a, b, z)/GAMMA(b)= sum((pochhammer(a, s))/(GAMMA(b + s)factorial(s))(z)^(s), s = 0..infinity)`	`Hypergeometric1F1Regularized[a, b, z]= Sum[Divide[Pochhammer[a, s],Gamma[b + s](s)!](z)^(s), {s, 0, Infinity}]`	Successful	Successful	-	-
13.2.E4	${\displaystyle{\displaystyle M\left(a,b,z\right)=\Gamma\left(b\right){\mathbf{% M}}\left(a,b,z\right)}}$	`KummerM(a, b, z)= GAMMA(b)*KummerM(a, b, z)/GAMMA(b)`	`Hypergeometric1F1[a, b, z]= Gamma[b]*Hypergeometric1F1Regularized[a, b, z]`	Successful	Successful	-	-
13.2.E5	${\displaystyle{\displaystyle\lim_{b\to-n}\frac{M\left(a,b,z\right)}{\Gamma% \left(b\right)}={\mathbf{M}}\left(a,-n,z\right)}}$	`limit((KummerM(a, b, z))/(GAMMA(b)), b = - n)= KummerM(a, - n, z)/GAMMA(- n)`	`Limit[Divide[Hypergeometric1F1[a, b, z],Gamma[b]], b -> - n]= Hypergeometric1F1Regularized[a, - n, z]`	Successful	Successful	-	-
13.2.E5	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,-n,z\right)=\frac{{\left(a% \right)_{n+1}}}{(n+1)!}z^{n+1}M\left(a+n+1,n+2,z\right)}}$	`KummerM(a, - n, z)/GAMMA(- n)=(pochhammer(a, n + 1))/(factorial(n + 1))(z)^(n + 1) KummerM(a + n + 1, n + 2, z)`	`Hypergeometric1F1Regularized[a, - n, z]=Divide[Pochhammer[a, n + 1],(n + 1)!](z)^(n + 1) Hypergeometric1F1[a + n + 1, n + 2, z]`	Failure	Failure	Fail `Float(undefined)+Float(undefined)I <- {a = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `Float(undefined)+Float(undefined)I <- {a = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `Float(undefined)+Float(undefined)I <- {a = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `Float(undefined)+Float(undefined)I <- {a = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Successful
13.2.E7	${\displaystyle{\displaystyle U\left(-m,b,z\right)=(-1)^{m}{\left(b\right)_{m}}% M\left(-m,b,z\right)}}$	`KummerU(- m, b, z)=(- 1)^(m)* pochhammer(b, m)*KummerM(- m, b, z)`	`HypergeometricU[- m, b, z]=(- 1)^(m)* Pochhammer[b, m]*Hypergeometric1F1[- m, b, z]`	Failure	Failure	Skip	Successful
13.2.E7	${\displaystyle{\displaystyle(-1)^{m}{\left(b\right)_{m}}M\left(-m,b,z\right)=(% -1)^{m}\sum_{s=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{s}{\left(b+s\right)_{m-s}}(-z)% ^{s}}}$	`(- 1)^(m)* pochhammer(b, m)KummerM(- m, b, z)=(- 1)^(m) sum(binomial(m,s)pochhammer(b + s, m - s)(- z)^(s), s = 0..m)`	`(- 1)^(m)* Pochhammer[b, m]Hypergeometric1F1[- m, b, z]=(- 1)^(m) Sum[Binomial[m,s]Pochhammer[b + s, m - s](- z)^(s), {s, 0, m}]`	Successful	Successful	-	-
13.2.E8	${\displaystyle{\displaystyle U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-% n\right)_{n}}}{z^{a+n}}M\left(-n,1-a-n,z\right)}}$	`KummerU(a, a + n + 1, z)=((- 1)^(n)* pochhammer(1 - a - n, n))/((z)^(a + n))*KummerM(- n, 1 - a - n, z)`	`HypergeometricU[a, a + n + 1, z]=Divide[(- 1)^(n)* Pochhammer[1 - a - n, n],(z)^(a + n)]*Hypergeometric1F1[- n, 1 - a - n, z]`	Failure	Failure	Skip	Successful
13.2.E8	${\displaystyle{\displaystyle\frac{(-1)^{n}{\left(1-a-n\right)_{n}}}{z^{a+n}}M% \left(-n,1-a-n,z\right)=z^{-a}\sum_{s=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{s}{% \left(a\right)_{s}}z^{-s}}}$	`((- 1)^(n)* pochhammer(1 - a - n, n))/((z)^(a + n))KummerM(- n, 1 - a - n, z)= (z)^(- a) sum(binomial(n,s)pochhammer(a, s)(z)^(- s), s = 0..n)`	`Divide[(- 1)^(n)* Pochhammer[1 - a - n, n],(z)^(a + n)]Hypergeometric1F1[- n, 1 - a - n, z]= (z)^(- a) Sum[Binomial[n,s]Pochhammer[a, s](z)^(- s), {s, 0, n}]`	Failure	Failure	Skip	Successful
13.2.E9	${\displaystyle{\displaystyle U\left(a,n+1,z\right)=\frac{(-1)^{n+1}}{n!\Gamma% \left(a-n\right)}\sum_{k=0}^{\infty}\frac{{\left(a\right)_{k}}}{{\left(n+1% \right)_{k}}k!}z^{k}\left(\ln z+\psi\left(a+k\right)-\psi\left(1+k\right)-\psi% \left(n+k+1\right)\right)+\frac{1}{\Gamma\left(a\right)}\sum_{k=1}^{n}\frac{(k% -1)!{\left(1-a+k\right)_{n-k}}}{(n-k)!}z^{-k}}}$	`KummerU(a, n + 1, z)=((- 1)^(n + 1))/(factorial(n)GAMMA(a - n))sum((pochhammer(a, k))/(pochhammer(n + 1, k)factorial(k))(z)^(k)(ln(z)+ Psi(a + k)- Psi(1 + k)- Psi(n + k + 1)), k = 0..infinity)+(1)/(GAMMA(a))sum((factorial(k - 1)pochhammer(1 - a + k, n - k))/(factorial(n - k))(z)^(- k), k = 1..n)`	`HypergeometricU[a, n + 1, z]=Divide[(- 1)^(n + 1),(n)!Gamma[a - n]]Sum[Divide[Pochhammer[a, k],Pochhammer[n + 1, k](k)!](z)^(k)(Log[z]+ PolyGamma[a + k]- PolyGamma[1 + k]- PolyGamma[n + k + 1]), {k, 0, Infinity}]+Divide[1,Gamma[a]]Sum[Divide[(k - 1)!Pochhammer[1 - a + k, n - k],(n - k)!](z)^(- k), {k, 1, n}]`	Error	Failure	-	Error
13.2.E10	${\displaystyle{\displaystyle U\left(-m,n+1,z\right)=(-1)^{m}{\left(n+1\right)_% {m}}M\left(-m,n+1,z\right)}}$	`KummerU(- m, n + 1, z)=(- 1)^(m)* pochhammer(n + 1, m)*KummerM(- m, n + 1, z)`	`HypergeometricU[- m, n + 1, z]=(- 1)^(m)* Pochhammer[n + 1, m]*Hypergeometric1F1[- m, n + 1, z]`	Failure	Failure	Successful	Successful
13.2.E10	${\displaystyle{\displaystyle(-1)^{m}{\left(n+1\right)_{m}}M\left(-m,n+1,z% \right)=(-1)^{m}\sum_{s=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{s}{\left(n+s+1\right)% _{m-s}}(-z)^{s}}}$	`(- 1)^(m)* pochhammer(n + 1, m)KummerM(- m, n + 1, z)=(- 1)^(m) sum(binomial(m,s)pochhammer(n + s + 1, m - s)(- z)^(s), s = 0..m)`	`(- 1)^(m)* Pochhammer[n + 1, m]Hypergeometric1F1[- m, n + 1, z]=(- 1)^(m) Sum[Binomial[m,s]Pochhammer[n + s + 1, m - s](- z)^(s), {s, 0, m}]`	Successful	Successful	-	-
13.2.E11	${\displaystyle{\displaystyle U\left(a,-n,z\right)=z^{n+1}U\left(a+n+1,n+2,z% \right)}}$	`KummerU(a, - n, z)= (z)^(n + 1)* KummerU(a + n + 1, n + 2, z)`	`HypergeometricU[a, - n, z]= (z)^(n + 1)* HypergeometricU[a + n + 1, n + 2, z]`	Successful	Successful	-	-
13.2.E12	${\displaystyle{\displaystyle U\left(a,b,ze^{2\pi\mathrm{i}m}\right)=\frac{2\pi% \mathrm{i}e^{-\pi\mathrm{i}bm}\sin\left(\pi bm\right)}{\Gamma\left(1+a-b\right% )\sin\left(\pi b\right)}{\mathbf{M}}\left(a,b,z\right)+e^{-2\pi\mathrm{i}bm}U% \left(a,b,z\right)}}$	`KummerU(a, b, zexp(2PiIm))=(2PiIexp(- PiIbm)sin(Pibm))/(GAMMA(1 + a - b)sin(Pib))KummerM(a, b, z)/GAMMA(b)+ exp(- 2PiIbm)*KummerU(a, b, z)`	`HypergeometricU[a, b, zExp[2PiIm]]=Divide[2PiIExp[- PiIbm]Sin[Pibm],Gamma[1 + a - b]Sin[Pib]]Hypergeometric1F1Regularized[a, b, z]+ Exp[- 2PiIbm]*HypergeometricU[a, b, z]`	Failure	Failure	Fail `584.8702437+1098.665595I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 1}` `448650.07-8984458.84I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 2}` `-.361175805e11+.540703722e11I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 3}` `1655.171849-5530.515123I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), m = 1}` ... skip entries to safe data	Skip
13.2.E33	${\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),z% ^{1-b}{\mathbf{M}}\left(a-b+1,2-b,z\right)\right\}=\sin\left(\pi b\right)z^{-b% }e^{z}/\pi}}$	`(KummerM(a, b, z)/GAMMA(b))diff((z)^(1 - b) KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)-diff(KummerM(a, b, z)/GAMMA(b), z)((z)^(1 - b) KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))= sin(Pib)(z)^(- b)* exp(z)/ Pi`	`Wronskian[{Hypergeometric1F1Regularized[a, b, z], (z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z]}, z]= Sin[Pib](z)^(- b)* Exp[z]/ Pi`	Failure	Failure	Successful	Skip
13.2.E34	${\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),U% \left(a,b,z\right)\right\}=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a\right)}}}$	`(KummerM(a, b, z)/GAMMA(b))diff(KummerU(a, b, z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)(KummerU(a, b, z))= -((z)^(- b)* exp(z))/(GAMMA(a))`	`Wronskian[{Hypergeometric1F1Regularized[a, b, z], HypergeometricU[a, b, z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[a]]`	Failure	Failure	Successful	Skip
13.2.E35	${\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),e% ^{z}U\left(b-a,b,e^{+\pi\mathrm{i}}z\right)\right\}=\ifrac{e^{-b\pi\mathrm{i}}% z^{-b}e^{z}}{\Gamma\left(b-a\right)}}}$	`(KummerM(a, b, z)/GAMMA(b))diff(exp(z)KummerU(b - a, b, exp(+ PiI)z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)(exp(z)KummerU(b - a, b, exp(+ PiI)z))=(exp(- bPiI)(z)^(- b) exp(z))/(GAMMA(b - a))`	`Wronskian[{Hypergeometric1F1Regularized[a, b, z], Exp[z]HypergeometricU[b - a, b, Exp[+ PiI]z]}, z]=Divide[Exp[- bPiI](z)^(- b)* Exp[z],Gamma[b - a]]`	Failure	Failure	Skip	Skip
13.2.E35	${\displaystyle{\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),e% ^{z}U\left(b-a,b,e^{-\pi\mathrm{i}}z\right)\right\}=\ifrac{e^{+b\pi\mathrm{i}}% z^{-b}e^{z}}{\Gamma\left(b-a\right)}}}$	`(KummerM(a, b, z)/GAMMA(b))diff(exp(z)KummerU(b - a, b, exp(- PiI)z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)(exp(z)KummerU(b - a, b, exp(- PiI)z))=(exp(+ bPiI)(z)^(- b) exp(z))/(GAMMA(b - a))`	`Wronskian[{Hypergeometric1F1Regularized[a, b, z], Exp[z]HypergeometricU[b - a, b, Exp[- PiI]z]}, z]=Divide[Exp[+ bPiI](z)^(- b)* Exp[z],Gamma[b - a]]`	Failure	Failure	Skip	Skip
13.2.E36	${\displaystyle{\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2% -b,z\right),U\left(a,b,z\right)\right\}=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a-b+1% \right)}}}$	`((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))diff(KummerU(a, b, z), z)-diff((z)^(1 - b) KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)(KummerU(a, b, z))= -((z)^(- b) exp(z))/(GAMMA(a - b + 1))`	`Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], HypergeometricU[a, b, z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[a - b + 1]]`	Failure	Failure	Skip	Skip
13.2.E37	${\displaystyle{\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2% -b,z\right),e^{z}U\left(b-a,b,e^{+\pi\mathrm{i}}z\right)\right\}=-\ifrac{z^{-b% }e^{z}}{\Gamma\left(1-a\right)}}}$	`((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))diff(exp(z)KummerU(b - a, b, exp(+ PiI)z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)(exp(z)KummerU(b - a, b, exp(+ PiI)z))= -((z)^(- b)* exp(z))/(GAMMA(1 - a))`	`Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], Exp[z]HypergeometricU[b - a, b, Exp[+ PiI]z]}, z]= -Divide[(z)^(- b) Exp[z],Gamma[1 - a]]`	Failure	Failure	Skip	Successful
13.2.E37	${\displaystyle{\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2% -b,z\right),e^{z}U\left(b-a,b,e^{-\pi\mathrm{i}}z\right)\right\}=-\ifrac{z^{-b% }e^{z}}{\Gamma\left(1-a\right)}}}$	`((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))diff(exp(z)KummerU(b - a, b, exp(- PiI)z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)(exp(z)KummerU(b - a, b, exp(- PiI)z))= -((z)^(- b)* exp(z))/(GAMMA(1 - a))`	`Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], Exp[z]HypergeometricU[b - a, b, Exp[- PiI]z]}, z]= -Divide[(z)^(- b) Exp[z],Gamma[1 - a]]`	Failure	Failure	Skip	Skip
13.2.E38	${\displaystyle{\displaystyle\mathscr{W}\left\{U\left(a,b,z\right),e^{z}U\left(% b-a,b,e^{+\pi\mathrm{i}}z\right)\right\}=e^{+(a-b)\pi\mathrm{i}}z^{-b}e^{z}}}$	`(KummerU(a, b, z))diff(exp(z)KummerU(b - a, b, exp(+ PiI)z), z)-diff(KummerU(a, b, z), z)(exp(z)KummerU(b - a, b, exp(+ PiI)z))= exp(+(a - b)* PiI)(z)^(- b)* exp(z)`	`Wronskian[{HypergeometricU[a, b, z], Exp[z]HypergeometricU[b - a, b, Exp[+ PiI]z]}, z]= Exp[+(a - b) PiI](z)^(- b)* Exp[z]`	Failure	Failure	Skip	Fail `Complex[1040.14465936905, 3523.550863963589] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[13.933478379950422, -18.985981055998398] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[16167.755810004226, 20483.57845334895] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-167.2507901552425, 2.9337620233109254] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.2.E38	${\displaystyle{\displaystyle\mathscr{W}\left\{U\left(a,b,z\right),e^{z}U\left(% b-a,b,e^{-\pi\mathrm{i}}z\right)\right\}=e^{-(a-b)\pi\mathrm{i}}z^{-b}e^{z}}}$	`(KummerU(a, b, z))diff(exp(z)KummerU(b - a, b, exp(- PiI)z), z)-diff(KummerU(a, b, z), z)(exp(z)KummerU(b - a, b, exp(- PiI)z))= exp(-(a - b)* PiI)(z)^(- b)* exp(z)`	`Wronskian[{HypergeometricU[a, b, z], Exp[z]HypergeometricU[b - a, b, Exp[- PiI]z]}, z]= Exp[-(a - b) PiI](z)^(- b)* Exp[z]`	Failure	Failure	Skip	Fail `Complex[-26409.287510504182, -21215.250458979182] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[17917.63845480152, -4449.098851771366] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[128856.58558615872, -203204.6357206061] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-130654.53246573739, 11199.95676626326] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.2.E39	${\displaystyle{\displaystyle M\left(a,b,z\right)=e^{z}M\left(b-a,b,-z\right)}}$	`KummerM(a, b, z)= exp(z)*KummerM(b - a, b, - z)`	`Hypergeometric1F1[a, b, z]= Exp[z]*Hypergeometric1F1[b - a, b, - z]`	Failure	Successful	Successful	-
13.2.E40	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{1-b}U\left(a-b+1,2-b,z% \right)}}$	`KummerU(a, b, z)= (z)^(1 - b)* KummerU(a - b + 1, 2 - b, z)`	`HypergeometricU[a, b, z]= (z)^(1 - b)* HypergeometricU[a - b + 1, 2 - b, z]`	Successful	Successful	-	-
13.2.E41	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(b\right)}M\left(a,b,z\right)=% \frac{e^{-a\pi\mathrm{i}}}{\Gamma\left(b-a\right)}U\left(a,b,z\right)+\frac{e^% {+(b-a)\pi\mathrm{i}}}{\Gamma\left(a\right)}e^{z}U\left(b-a,b,e^{+\pi\mathrm{i% }}z\right)}}$	`(1)/(GAMMA(b))KummerM(a, b, z)=(exp(- aPiI))/(GAMMA(b - a))KummerU(a, b, z)+(exp(+(b - a)* PiI))/(GAMMA(a))exp(z)KummerU(b - a, b, exp(+ PiI)*z)`	`Divide[1,Gamma[b]]Hypergeometric1F1[a, b, z]=Divide[Exp[- aPiI],Gamma[b - a]]HypergeometricU[a, b, z]+Divide[Exp[+(b - a)* PiI],Gamma[a]]Exp[z]HypergeometricU[b - a, b, Exp[+ PiI]*z]`	Failure	Failure	Fail `17637856.16+44349536.15I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `78404.04567+70170.88583I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `23503366.51-739194412.4I <- {a = 2^(1/2)+I2^(1/2), b = -2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-413147.5251+1810381.777I <- {a = 2^(1/2)+I2^(1/2), b = -2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Skip
13.2.E41	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(b\right)}M\left(a,b,z\right)=% \frac{e^{+a\pi\mathrm{i}}}{\Gamma\left(b-a\right)}U\left(a,b,z\right)+\frac{e^% {-(b-a)\pi\mathrm{i}}}{\Gamma\left(a\right)}e^{z}U\left(b-a,b,e^{-\pi\mathrm{i% }}z\right)}}$	`(1)/(GAMMA(b))KummerM(a, b, z)=(exp(+ aPiI))/(GAMMA(b - a))KummerU(a, b, z)+(exp(-(b - a)* PiI))/(GAMMA(a))exp(z)KummerU(b - a, b, exp(- PiI)*z)`	`Divide[1,Gamma[b]]Hypergeometric1F1[a, b, z]=Divide[Exp[+ aPiI],Gamma[b - a]]HypergeometricU[a, b, z]+Divide[Exp[-(b - a)* PiI],Gamma[a]]Exp[z]HypergeometricU[b - a, b, Exp[- PiI]*z]`	Failure	Failure	Fail `8.816149469+15.35727015I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `3.036467728-4.734652938I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `237.2244957-69.52948040I <- {a = 2^(1/2)+I2^(1/2), b = -2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `40.35920508+88.71475163I <- {a = 2^(1/2)+I2^(1/2), b = -2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` ... skip entries to safe data	Skip
13.2.E42	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{\Gamma\left(1-b\right)}% {\Gamma\left(a-b+1\right)}M\left(a,b,z\right)+\frac{\Gamma\left(b-1\right)}{% \Gamma\left(a\right)}z^{1-b}M\left(a-b+1,2-b,z\right)}}$	`KummerU(a, b, z)=(GAMMA(1 - b))/(GAMMA(a - b + 1))KummerM(a, b, z)+(GAMMA(b - 1))/(GAMMA(a))(z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)`	`HypergeometricU[a, b, z]=Divide[Gamma[1 - b],Gamma[a - b + 1]]Hypergeometric1F1[a, b, z]+Divide[Gamma[b - 1],Gamma[a]](z)^(1 - b)* Hypergeometric1F1[a - b + 1, 2 - b, z]`	Successful	Successful	-	-
13.3.E1	${\displaystyle{\displaystyle(b-a)M\left(a-1,b,z\right)+(2a-b+z)M\left(a,b,z% \right)-aM\left(a+1,b,z\right)=0}}$	`(b - a)* KummerM(a - 1, b, z)+(2a - b + z) KummerM(a, b, z)- a*KummerM(a + 1, b, z)= 0`	`(b - a)* Hypergeometric1F1[a - 1, b, z]+(2a - b + z) Hypergeometric1F1[a, b, z]- a*Hypergeometric1F1[a + 1, b, z]= 0`	Successful	Successful	-	-
13.3.E2	${\displaystyle{\displaystyle b(b-1)M\left(a,b-1,z\right)+b(1-b-z)M\left(a,b,z% \right)+z(b-a)M\left(a,b+1,z\right)=0}}$	`b(b - 1) KummerM(a, b - 1, z)+ b(1 - b - z) KummerM(a, b, z)+ z(b - a) KummerM(a, b + 1, z)= 0`	`b(b - 1) Hypergeometric1F1[a, b - 1, z]+ b(1 - b - z) Hypergeometric1F1[a, b, z]+ z(b - a) Hypergeometric1F1[a, b + 1, z]= 0`	Successful	Successful	-	-
13.3.E3	${\displaystyle{\displaystyle(a-b+1)M\left(a,b,z\right)-aM\left(a+1,b,z\right)+% (b-1)M\left(a,b-1,z\right)=0}}$	`(a - b + 1)* KummerM(a, b, z)- aKummerM(a + 1, b, z)+(b - 1) KummerM(a, b - 1, z)= 0`	`(a - b + 1)* Hypergeometric1F1[a, b, z]- aHypergeometric1F1[a + 1, b, z]+(b - 1) Hypergeometric1F1[a, b - 1, z]= 0`	Successful	Successful	-	-
13.3.E4	${\displaystyle{\displaystyle bM\left(a,b,z\right)-bM\left(a-1,b,z\right)-zM% \left(a,b+1,z\right)=0}}$	`bKummerM(a, b, z)- bKummerM(a - 1, b, z)- z*KummerM(a, b + 1, z)= 0`	`bHypergeometric1F1[a, b, z]- bHypergeometric1F1[a - 1, b, z]- z*Hypergeometric1F1[a, b + 1, z]= 0`	Successful	Successful	-	-
13.3.E5	${\displaystyle{\displaystyle b(a+z)M\left(a,b,z\right)+z(a-b)M\left(a,b+1,z% \right)-abM\left(a+1,b,z\right)=0}}$	`b(a + z) KummerM(a, b, z)+ z(a - b) KummerM(a, b + 1, z)- abKummerM(a + 1, b, z)= 0`	`b(a + z) Hypergeometric1F1[a, b, z]+ z(a - b) Hypergeometric1F1[a, b + 1, z]- abHypergeometric1F1[a + 1, b, z]= 0`	Successful	Successful	-	-
13.3.E6	${\displaystyle{\displaystyle(a-1+z)M\left(a,b,z\right)+(b-a)M\left(a-1,b,z% \right)+(1-b)M\left(a,b-1,z\right)=0}}$	`(a - 1 + z)* KummerM(a, b, z)+(b - a)* KummerM(a - 1, b, z)+(1 - b)* KummerM(a, b - 1, z)= 0`	`(a - 1 + z)* Hypergeometric1F1[a, b, z]+(b - a)* Hypergeometric1F1[a - 1, b, z]+(1 - b)* Hypergeometric1F1[a, b - 1, z]= 0`	Successful	Successful	-	-
13.3.E7	${\displaystyle{\displaystyle U\left(a-1,b,z\right)+(b-2a-z)U\left(a,b,z\right)% +a(a-b+1)U\left(a+1,b,z\right)=0}}$	`KummerU(a - 1, b, z)+(b - 2a - z) KummerU(a, b, z)+ a(a - b + 1) KummerU(a + 1, b, z)= 0`	`HypergeometricU[a - 1, b, z]+(b - 2a - z) HypergeometricU[a, b, z]+ a(a - b + 1) HypergeometricU[a + 1, b, z]= 0`	Successful	Successful	-	-
13.3.E8	${\displaystyle{\displaystyle(b-a-1)U\left(a,b-1,z\right)+(1-b-z)U\left(a,b,z% \right)+zU\left(a,b+1,z\right)=0}}$	`(b - a - 1)* KummerU(a, b - 1, z)+(1 - b - z)* KummerU(a, b, z)+ z*KummerU(a, b + 1, z)= 0`	`(b - a - 1)* HypergeometricU[a, b - 1, z]+(1 - b - z)* HypergeometricU[a, b, z]+ z*HypergeometricU[a, b + 1, z]= 0`	Successful	Successful	-	-
13.3.E9	${\displaystyle{\displaystyle U\left(a,b,z\right)-aU\left(a+1,b,z\right)-U\left% (a,b-1,z\right)=0}}$	`KummerU(a, b, z)- a*KummerU(a + 1, b, z)- KummerU(a, b - 1, z)= 0`	`HypergeometricU[a, b, z]- a*HypergeometricU[a + 1, b, z]- HypergeometricU[a, b - 1, z]= 0`	Successful	Successful	-	-
13.3.E10	${\displaystyle{\displaystyle(b-a)U\left(a,b,z\right)+U\left(a-1,b,z\right)-zU% \left(a,b+1,z\right)=0}}$	`(b - a)* KummerU(a, b, z)+ KummerU(a - 1, b, z)- z*KummerU(a, b + 1, z)= 0`	`(b - a)* HypergeometricU[a, b, z]+ HypergeometricU[a - 1, b, z]- z*HypergeometricU[a, b + 1, z]= 0`	Successful	Successful	-	-
13.3.E11	${\displaystyle{\displaystyle(a+z)U\left(a,b,z\right)-zU\left(a,b+1,z\right)+a(% b-a-1)U\left(a+1,b,z\right)=0}}$	`(a + z)* KummerU(a, b, z)- zKummerU(a, b + 1, z)+ a(b - a - 1)* KummerU(a + 1, b, z)= 0`	`(a + z)* HypergeometricU[a, b, z]- zHypergeometricU[a, b + 1, z]+ a(b - a - 1)* HypergeometricU[a + 1, b, z]= 0`	Successful	Successful	-	-
13.3.E12	${\displaystyle{\displaystyle(a-1+z)U\left(a,b,z\right)-U\left(a-1,b,z\right)+(% a-b+1)U\left(a,b-1,z\right)=0}}$	`(a - 1 + z)* KummerU(a, b, z)- KummerU(a - 1, b, z)+(a - b + 1)* KummerU(a, b - 1, z)= 0`	`(a - 1 + z)* HypergeometricU[a, b, z]- HypergeometricU[a - 1, b, z]+(a - b + 1)* HypergeometricU[a, b - 1, z]= 0`	Successful	Successful	-	-
13.3.E13	${\displaystyle{\displaystyle(a+1)zM\left(a+2,b+2,z\right)+(b+1)(b-z)M\left(a+1% ,b+1,z\right)-b(b+1)M\left(a,b,z\right)=0}}$	`(a + 1)* zKummerM(a + 2, b + 2, z)+(b + 1)(b - z)* KummerM(a + 1, b + 1, z)- b(b + 1) KummerM(a, b, z)= 0`	`(a + 1)* zHypergeometric1F1[a + 2, b + 2, z]+(b + 1)(b - z)* Hypergeometric1F1[a + 1, b + 1, z]- b(b + 1) Hypergeometric1F1[a, b, z]= 0`	Successful	Successful	-	-
13.3.E14	${\displaystyle{\displaystyle(a+1)zU\left(a+2,b+2,z\right)+(z-b)U\left(a+1,b+1,% z\right)-U\left(a,b,z\right)=0}}$	`(a + 1)* zKummerU(a + 2, b + 2, z)+(z - b) KummerU(a + 1, b + 1, z)- KummerU(a, b, z)= 0`	`(a + 1)* zHypergeometricU[a + 2, b + 2, z]+(z - b) HypergeometricU[a + 1, b + 1, z]- HypergeometricU[a, b, z]= 0`	Successful	Successful	-	-
13.3.E15	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}M\left(a,b,z\right)=% \frac{a}{b}M\left(a+1,b+1,z\right)}}$	`diff(KummerM(a, b, z), z)=(a)/(b)*KummerM(a + 1, b + 1, z)`	`D[Hypergeometric1F1[a, b, z], z]=Divide[a,b]*Hypergeometric1F1[a + 1, b + 1, z]`	Successful	Successful	-	-
13.3.E16	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}M\left(a% ,b,z\right)=\frac{{\left(a\right)_{n}}}{{\left(b\right)_{n}}}M\left(a+n,b+n,z% \right)}}$	`diff(KummerM(a, b, z), [z$(n)])=(pochhammer(a, n))/(pochhammer(b, n))*KummerM(a + n, b + n, z)`	`D[Hypergeometric1F1[a, b, z], {z, n}]=Divide[Pochhammer[a, n],Pochhammer[b, n]]*Hypergeometric1F1[a + n, b + n, z]`	Successful	Failure	-	Skip
13.3.E17	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{a-1}M\left(a,b,z\right)\right)={\left(a\right)_{n}}z^{a+n-1}M\left(a+% n,b,z\right)}}$	`(zdiff(z, z))^(n)((z)^(a - 1)* KummerM(a, b, z))= pochhammer(a, n)(z)^(a + n - 1) KummerM(a + n, b, z)`	`(zD[z, z])^(n)((z)^(a - 1)* Hypergeometric1F1[a, b, z])= Pochhammer[a, n](z)^(a + n - 1) Hypergeometric1F1[a + n, b, z]`	Failure	Failure	Fail `2.537884887+11.89104377I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-123.7627467+81.19826795I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-1555.783365-1131.870657I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `-1.589608076+60.84364464I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.3.E18	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}M\left(a,b,z\right)\right)={\left(b-n\right)_{n}}z^{b-n-1}M\left(a,b-n,z% \right)}}$	`diff((z)^(b - 1)* KummerM(a, b, z), [z$(n)])= pochhammer(b - n, n)(z)^(b - n - 1) KummerM(a, b - n, z)`	`D[(z)^(b - 1)* Hypergeometric1F1[a, b, z], {z, n}]= Pochhammer[b - n, n](z)^(b - n - 1) Hypergeometric1F1[a, b - n, z]`	Failure	Failure	Successful	Skip
13.3.E19	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{b-a-1}e^{-z}M\left(a,b,z\right)\right)={\left(b-a\right)_{n}}z^{b-a+n% -1}e^{-z}M\left(a-n,b,z\right)}}$	`(zdiff(z, z))^(n)((z)^(b - a - 1)* exp(- z)KummerM(a, b, z))= pochhammer(b - a, n)(z)^(b - a + n - 1)* exp(- z)*KummerM(a - n, b, z)`	`(zD[z, z])^(n)((z)^(b - a - 1)* Exp[- z]Hypergeometric1F1[a, b, z])= Pochhammer[b - a, n](z)^(b - a + n - 1)* Exp[- z]*Hypergeometric1F1[a - n, b, z]`	Failure	Failure	Fail `1.000000000+0.I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `1.414213562+1.414213562I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `0.+3.999999998I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `1.000000000+0.I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.3.E20	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-z}M\left(a,b,z\right)\right)=(-1)^{n}\frac{{\left(b-a\right)_{n}}}{{\left(b% \right)_{n}}}e^{-z}M\left(a,b+n,z\right)}}$	`diff(exp(- z)KummerM(a, b, z), [z$(n)])=(- 1)^(n)(pochhammer(b - a, n))/(pochhammer(b, n))exp(- z)KummerM(a, b + n, z)`	`D[Exp[- z]Hypergeometric1F1[a, b, z], {z, n}]=(- 1)^(n)Divide[Pochhammer[b - a, n],Pochhammer[b, n]]Exp[- z]Hypergeometric1F1[a, b + n, z]`	Failure	Failure	Successful	Skip
13.3.E21	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}e^{-z}M\left(a,b,z\right)\right)={\left(b-n\right)_{n}}z^{b-n-1}e^{-z}M% \left(a-n,b-n,z\right)}}$	`diff((z)^(b - 1)* exp(- z)KummerM(a, b, z), [z$(n)])= pochhammer(b - n, n)(z)^(b - n - 1)* exp(- z)*KummerM(a - n, b - n, z)`	`D[(z)^(b - 1)* Exp[- z]Hypergeometric1F1[a, b, z], {z, n}]= Pochhammer[b - n, n](z)^(b - n - 1)* Exp[- z]*Hypergeometric1F1[a - n, b - n, z]`	Failure	Failure	Skip	Error
13.3.E22	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}U\left(a,b,z\right)=% -aU\left(a+1,b+1,z\right)}}$	`diff(KummerU(a, b, z), z)= - a*KummerU(a + 1, b + 1, z)`	`D[HypergeometricU[a, b, z], z]= - a*HypergeometricU[a + 1, b + 1, z]`	Successful	Successful	-	-
13.3.E23	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}U\left(a% ,b,z\right)=(-1)^{n}{\left(a\right)_{n}}U\left(a+n,b+n,z\right)}}$	`diff(KummerU(a, b, z), [z$(n)])=(- 1)^(n)* pochhammer(a, n)*KummerU(a + n, b + n, z)`	`D[HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Pochhammer[a, n]*HypergeometricU[a + n, b + n, z]`	Failure	Successful	Skip	-
13.3.E24	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{a-1}U\left(a,b,z\right)\right)={\left(a\right)_{n}}{\left(a-b+1\right% )_{n}}z^{a+n-1}U\left(a+n,b,z\right)}}$	`(zdiff(z, z))^(n)((z)^(a - 1)* KummerU(a, b, z))= pochhammer(a, n)pochhammer(a - b + 1, n)(z)^(a + n - 1)* KummerU(a + n, b, z)`	`(zD[z, z])^(n)((z)^(a - 1)* HypergeometricU[a, b, z])= Pochhammer[a, n]Pochhammer[a - b + 1, n](z)^(a + n - 1)* HypergeometricU[a + n, b, z]`	Failure	Failure	Fail `.3178044521-.5812355890e-1I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `.5638915996+.3833395878I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `.2833587160+.898459259I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `.2659178351-.5754539144I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.3.E25	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}U\left(a,b,z\right)\right)=(-1)^{n}{\left(a-b+1\right)_{n}}z^{b-n-1}U% \left(a,b-n,z\right)}}$	`diff((z)^(b - 1)* KummerU(a, b, z), [z$(n)])=(- 1)^(n)* pochhammer(a - b + 1, n)(z)^(b - n - 1) KummerU(a, b - n, z)`	`D[(z)^(b - 1)* HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Pochhammer[a - b + 1, n](z)^(b - n - 1) HypergeometricU[a, b - n, z]`	Failure	Failure	Skip	Skip
13.3.E26	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{b-a-1}e^{-z}U\left(a,b,z\right)\right)=(-1)^{n}z^{b-a+n-1}e^{-z}U% \left(a-n,b,z\right)}}$	`(zdiff(z, z))^(n)((z)^(b - a - 1)* exp(- z)KummerU(a, b, z))=(- 1)^(n) (z)^(b - a + n - 1)* exp(- z)*KummerU(a - n, b, z)`	`(zD[z, z])^(n)((z)^(b - a - 1)* Exp[- z]HypergeometricU[a, b, z])=(- 1)^(n) (z)^(b - a + n - 1)* Exp[- z]*HypergeometricU[a - n, b, z]`	Failure	Failure	Fail `-.6426838098-.1638932643I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-2.885602225+1.867279788I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-8.024434137+19.17405510I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `.5784828818e-1+.5986041895e-1I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.3.E27	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-z}U\left(a,b,z\right)\right)=(-1)^{n}e^{-z}U\left(a,b+n,z\right)}}$	`diff(exp(- z)KummerU(a, b, z), [z$(n)])=(- 1)^(n) exp(- z)*KummerU(a, b + n, z)`	`D[Exp[- z]HypergeometricU[a, b, z], {z, n}]=(- 1)^(n) Exp[- z]*HypergeometricU[a, b + n, z]`	Failure	Failure	Skip	Skip
13.3.E28	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}e^{-z}U\left(a,b,z\right)\right)=(-1)^{n}z^{b-n-1}e^{-z}U\left(a-n,b-n,z% \right)}}$	`diff((z)^(b - 1)* exp(- z)KummerU(a, b, z), [z$(n)])=(- 1)^(n) (z)^(b - n - 1)* exp(- z)*KummerU(a - n, b - n, z)`	`D[(z)^(b - 1)* Exp[- z]HypergeometricU[a, b, z], {z, n}]=(- 1)^(n) (z)^(b - n - 1)* Exp[- z]*HypergeometricU[a - n, b - n, z]`	Error	Failure	-	Error
13.3.E29	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}=% z^{n}\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}z^{n}}}$	`(zdiff(z, z))^(n)= (z)^(n) diff((z)^(n), [z$(n)])`	`(zD[z, z])^(n)= (z)^(n) D[(z)^(n), {z, n}]`	Failure	Failure	Fail `28.28427122-28.28427122I <- {z = 2^(1/2)+I2^(1/2), n = 3}` `28.28427122+28.28427122I <- {z = 2^(1/2)-I2^(1/2), n = 3}` `-28.28427122+28.28427122I <- {z = -2^(1/2)-I2^(1/2), n = 3}` `-28.28427122-28.28427122I <- {z = -2^(1/2)+I2^(1/2), n = 3}`	Fail `Complex[28.284271247461902, -28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[28.284271247461902, 28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-28.284271247461902, 28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-28.284271247461902, -28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.4.E1	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{1}{\Gamma% \left(a\right)\Gamma\left(b-a\right)}\int_{0}^{1}e^{zt}t^{a-1}(1-t)^{b-a-1}% \mathrm{d}t}}$	`KummerM(a, b, z)/GAMMA(b)=(1)/(GAMMA(a)GAMMA(b - a))int(exp(zt)(t)^(a - 1)*(1 - t)^(b - a - 1), t = 0..1)`	`Hypergeometric1F1Regularized[a, b, z]=Divide[1,Gamma[a]Gamma[b - a]]Integrate[Exp[zt](t)^(a - 1)*(1 - t)^(b - a - 1), {t, 0, 1}]`	Successful	Failure	-	Skip
13.4.E2	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{1}{\Gamma% \left(b-c\right)}\int_{0}^{1}{\mathbf{M}}\left(a,c,zt\right)t^{c-1}(1-t)^{b-c-% 1}\mathrm{d}t}}$	`KummerM(a, b, z)/GAMMA(b)=(1)/(GAMMA(b - c))int(KummerM(a, c, zt)/GAMMA(c)(t)^(c - 1)(1 - t)^(b - c - 1), t = 0..1)`	`Hypergeometric1F1Regularized[a, b, z]=Divide[1,Gamma[b - c]]Integrate[Hypergeometric1F1Regularized[a, c, zt](t)^(c - 1)(1 - t)^(b - c - 1), {t, 0, 1}]`	Successful	Failure	-	Skip
13.4.E3	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{z^{\frac{1}{% 2}-\frac{1}{2}b}}{\Gamma\left(a\right)}\int_{0}^{\infty}e^{-t}t^{a-\frac{1}{2}% b-\frac{1}{2}}J_{b-1}\left(2\sqrt{zt}\right)\mathrm{d}t}}$	`KummerM(a, b, - z)/GAMMA(b)=((z)^((1)/(2)-(1)/(2)b))/(GAMMA(a))int(exp(- t)(t)^(a -(1)/(2)b -(1)/(2))* BesselJ(b - 1, 2sqrt(zt)), t = 0..infinity)`	`Hypergeometric1F1Regularized[a, b, - z]=Divide[(z)^(Divide[1,2]-Divide[1,2]b),Gamma[a]]Integrate[Exp[- t](t)^(a -Divide[1,2]b -Divide[1,2])* BesselJ[b - 1, 2Sqrt[zt]], {t, 0, Infinity}]`	Failure	Failure	Skip	Error
13.4.E4	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{1}{\Gamma\left(a\right)% }\int_{0}^{\infty}e^{-zt}t^{a-1}(1+t)^{b-a-1}\mathrm{d}t}}$	`KummerU(a, b, z)=(1)/(GAMMA(a))int(exp(- zt)(t)^(a - 1)(1 + t)^(b - a - 1), t = 0..infinity)`	`HypergeometricU[a, b, z]=Divide[1,Gamma[a]]Integrate[Exp[- zt](t)^(a - 1)(1 + t)^(b - a - 1), {t, 0, Infinity}]`	Successful	Failure	-	Error
13.4.E5	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{z^{1-a}}{\Gamma\left(a% \right)\Gamma\left(1+a-b\right)}\int_{0}^{\infty}\frac{U\left(b-a,b,t\right)e^% {-t}t^{a-1}}{t+z}\mathrm{d}t}}$	`KummerU(a, b, z)=((z)^(1 - a))/(GAMMA(a)GAMMA(1 + a - b))int((KummerU(b - a, b, t)exp(- t)(t)^(a - 1))/(t + z), t = 0..infinity)`	`HypergeometricU[a, b, z]=Divide[(z)^(1 - a),Gamma[a]Gamma[1 + a - b]]Integrate[Divide[HypergeometricU[b - a, b, t]Exp[- t](t)^(a - 1),t + z], {t, 0, Infinity}]`	Failure	Failure	Skip	Error
13.4.E6	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{(-1)^{n}z^{1-b-n}}{% \Gamma\left(1+a-b\right)}\int_{0}^{\infty}\frac{{\mathbf{M}}\left(b-a,b,t% \right)e^{-t}t^{b+n-1}}{t+z}\mathrm{d}t}}$	`KummerU(a, b, z)=((- 1)^(n)* (z)^(1 - b - n))/(GAMMA(1 + a - b))int((KummerM(b - a, b, t)/GAMMA(b)exp(- t)*(t)^(b + n - 1))/(t + z), t = 0..infinity)`	`HypergeometricU[a, b, z]=Divide[(- 1)^(n)* (z)^(1 - b - n),Gamma[1 + a - b]]Integrate[Divide[Hypergeometric1F1Regularized[b - a, b, t]Exp[- t]*(t)^(b + n - 1),t + z], {t, 0, Infinity}]`	Failure	Failure	Skip	Error
13.4.E7	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{2z^{\frac{1}{2}-\frac{1% }{2}b}}{\Gamma\left(a\right)\Gamma\left(a-b+1\right)}\*\int_{0}^{\infty}e^{-t}% t^{a-\frac{1}{2}b-\frac{1}{2}}K_{b-1}\left(2\sqrt{zt}\right)\mathrm{d}t}}$	`KummerU(a, b, z)=(2(z)^((1)/(2)-(1)/(2)b))/(GAMMA(a)GAMMA(a - b + 1)) int(exp(- t)(t)^(a -(1)/(2)b -(1)/(2))* BesselK(b - 1, 2sqrt(zt)), t = 0..infinity)`	`HypergeometricU[a, b, z]=Divide[2(z)^(Divide[1,2]-Divide[1,2]b),Gamma[a]Gamma[a - b + 1]] Integrate[Exp[- t](t)^(a -Divide[1,2]b -Divide[1,2])* BesselK[b - 1, 2Sqrt[zt]], {t, 0, Infinity}]`	Successful	Failure	-	Error
13.4.E8	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{c-a}\*\int_{0}^{\infty}e^{% -zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left(a,a-b+1;c;-t\right)\mathrm{d}t}}$	`KummerU(a, b, z)= (z)^(c - a)* int(exp(- zt)(t)^(c - 1)* hypergeom([a , a - b + 1], [c], - t), t = 0..infinity)`	`HypergeometricU[a, b, z]= (z)^(c - a)* Integrate[Exp[- zt](t)^(c - 1)* HypergeometricPFQRegularized[{a , a - b + 1}, {c}, - t], {t, 0, Infinity}]`	Failure	Failure	Skip	Error
13.4.E9	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{\Gamma\left(1% +a-b\right)}{2\pi\mathrm{i}\Gamma\left(a\right)}\int_{0}^{(1+)}e^{zt}t^{a-1}{(% t-1)^{b-a-1}}\mathrm{d}t}}$	`KummerM(a, b, z)/GAMMA(b)=(GAMMA(1 + a - b))/(2PiIGAMMA(a))int(exp(zt)(t)^(a - 1)*(t - 1)^(b - a - 1), t = 0..(1 +))`	`Hypergeometric1F1Regularized[a, b, z]=Divide[Gamma[1 + a - b],2PiIGamma[a]]Integrate[Exp[zt](t)^(a - 1)*(t - 1)^(b - a - 1), {t, 0, (1 +)}]`	Error	Failure	-	Error
13.4.E10	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=e^{-a\pi\mathrm{i}}% \frac{\Gamma\left(1-a\right)}{2\pi\mathrm{i}\Gamma\left(b-a\right)}\int_{1}^{(% 0+)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\mathrm{d}t}}$	`KummerM(a, b, z)/GAMMA(b)= exp(- aPiI)(GAMMA(1 - a))/(2PiIGAMMA(b - a))int(exp(zt)(t)^(a - 1)(1 - t)^(b - a - 1), t = 1..(0 +))`	`Hypergeometric1F1Regularized[a, b, z]= Exp[- aPiI]Divide[Gamma[1 - a],2PiIGamma[b - a]]Integrate[Exp[zt](t)^(a - 1)(1 - t)^(b - a - 1), {t, 1, (0 +)}]`	Error	Failure	-	Error
13.4.E11	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=e^{-b\pi\mathrm{i}}% \Gamma\left(1-a\right)\Gamma\left(1+a-b\right)\*\frac{1}{4\pi^{2}}\int_{\alpha% }^{(0+,1+,0-,1-)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\mathrm{d}t}}$	`KummerM(a, b, z)/GAMMA(b)= exp(- bPiI)GAMMA(1 - a)GAMMA(1 + a - b)(1)/(4(Pi)^(2))int(exp(zt)(t)^(a - 1)(1 - t)^(b - a - 1), t = alpha..(0 + , 1 + , 0 - , 1 -))`	`Hypergeometric1F1Regularized[a, b, z]= Exp[- bPiI]Gamma[1 - a]Gamma[1 + a - b]Divide[1,4(Pi)^(2)]Integrate[Exp[zt](t)^(a - 1)(1 - t)^(b - a - 1), {t, \[Alpha], (0 + , 1 + , 0 - , 1 -)}]`	Error	Failure	-	Error
13.4.E12	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,c,z\right)=\frac{\Gamma\left(b% \right)}{2\pi\mathrm{i}}z^{1-b}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}{{}_{2}{% \mathbf{F}}_{1}}\left(a,b;c;\ifrac{1}{t}\right)\mathrm{d}t}}$	`KummerM(a, c, z)/GAMMA(c)=(GAMMA(b))/(2PiI)(z)^(1 - b) int(exp(zt)(t)^(- b)* hypergeom([a , b], [c], (1)/(t)), t = - infinity..(0 + , 1 +))`	`Hypergeometric1F1Regularized[a, c, z]=Divide[Gamma[b],2PiI](z)^(1 - b) Integrate[Exp[zt](t)^(- b)* HypergeometricPFQRegularized[{a , b}, {c}, Divide[1,t]], {t, - Infinity, (0 + , 1 +)}]`	Error	Failure	-	Error
13.4.E13	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{z^{1-b}}{2\pi% \mathrm{i}}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}\!\left(1-\frac{1}{t}\right)^{-% a}\mathrm{d}t}}$	`KummerM(a, b, z)/GAMMA(b)=((z)^(1 - b))/(2PiI)int(exp(zt)(t)^(- b)(1 -(1)/(t))^(- a), t = - infinity..(0 + , 1 +))`	`Hypergeometric1F1Regularized[a, b, z]=Divide[(z)^(1 - b),2PiI]Integrate[Exp[zt](t)^(- b)(1 -Divide[1,t])^(- a), {t, - Infinity, (0 + , 1 +)}]`	Error	Failure	-	Error
13.4.E14	${\displaystyle{\displaystyle U\left(a,b,z\right)=e^{-a\pi\mathrm{i}}\frac{% \Gamma\left(1-a\right)}{2\pi\mathrm{i}}\int_{\infty}^{(0+)}e^{-zt}t^{a-1}{(1+t% )^{b-a-1}}\mathrm{d}t}}$	`KummerU(a, b, z)= exp(- aPiI)(GAMMA(1 - a))/(2PiI)int(exp(- zt)(t)^(a - 1)*(1 + t)^(b - a - 1), t = infinity..(0 +))`	`HypergeometricU[a, b, z]= Exp[- aPiI]Divide[Gamma[1 - a],2PiI]Integrate[Exp[- zt](t)^(a - 1)*(1 + t)^(b - a - 1), {t, Infinity, (0 +)}]`	Error	Failure	-	Error
13.4.E15	${\displaystyle{\displaystyle\frac{U\left(a,b,z\right)}{\Gamma\left(c\right)% \Gamma\left(c-b+1\right)}=\frac{z^{1-c}}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e% ^{zt}t^{-c}{{}_{2}{\mathbf{F}}_{1}}\left(a,c;a+c-b+1;1-\frac{1}{t}\right)% \mathrm{d}t}}$	`(KummerU(a, b, z))/(GAMMA(c)GAMMA(c - b + 1))=((z)^(1 - c))/(2PiI)int(exp(zt)(t)^(- c)* hypergeom([a , c], [a + c - b + 1], 1 -(1)/(t)), t = - infinity..(0 +))`	`Divide[HypergeometricU[a, b, z],Gamma[c]Gamma[c - b + 1]]=Divide[(z)^(1 - c),2PiI]Integrate[Exp[zt](t)^(- c)* HypergeometricPFQRegularized[{a , c}, {a + c - b + 1}, 1 -Divide[1,t]], {t, - Infinity, (0 +)}]`	Error	Failure	-	Error
13.4.E16	${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{1}{2\pi% \mathrm{i}\Gamma\left(a\right)}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}% \frac{\Gamma\left(a+t\right)\Gamma\left(-t\right)}{\Gamma\left(b+t\right)}z^{t% }\mathrm{d}t}}$	`KummerM(a, b, - z)/GAMMA(b)=(1)/(2PiIGAMMA(a))int((GAMMA(a + t)GAMMA(- t))/(GAMMA(b + t))(z)^(t), t = - Iinfinity..Iinfinity)`	`Hypergeometric1F1Regularized[a, b, - z]=Divide[1,2PiIGamma[a]]Integrate[Divide[Gamma[a + t]Gamma[- t],Gamma[b + t]](z)^(t), {t, - IInfinity, IInfinity}]`	Failure	Failure	Skip	Error
13.4.E17	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{z^{-a}}{2\pi\mathrm{i}}% \int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(a+t\right)\Gamma% \left(1+a-b+t\right)\Gamma\left(-t\right)}{\Gamma\left(a\right)\Gamma\left(1+a% -b\right)}z^{-t}\mathrm{d}t}}$	`KummerU(a, b, z)=((z)^(- a))/(2PiI)int((GAMMA(a + t)GAMMA(1 + a - b + t)GAMMA(- t))/(GAMMA(a)GAMMA(1 + a - b))(z)^(- t), t = - Iinfinity..I*infinity)`	`HypergeometricU[a, b, z]=Divide[(z)^(- a),2PiI]Integrate[Divide[Gamma[a + t]Gamma[1 + a - b + t]Gamma[- t],Gamma[a]Gamma[1 + a - b]](z)^(- t), {t, - IInfinity, I*Infinity}]`	Failure	Failure	Skip	Error
13.4.E18	${\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{z^{1-b}e^{z}}{2\pi% \mathrm{i}}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(b-1+t% \right)\Gamma\left(t\right)}{\Gamma\left(a+t\right)}z^{-t}\mathrm{d}t}}$	`KummerU(a, b, z)=((z)^(1 - b)* exp(z))/(2PiI)int((GAMMA(b - 1 + t)GAMMA(t))/(GAMMA(a + t))(z)^(- t), t = - Iinfinity..I*infinity)`	`HypergeometricU[a, b, z]=Divide[(z)^(1 - b)* Exp[z],2PiI]Integrate[Divide[Gamma[b - 1 + t]Gamma[t],Gamma[a + t]](z)^(- t), {t, - IInfinity, I*Infinity}]`	Failure	Failure	Skip	Error
13.6.E1	${\displaystyle{\displaystyle M\left(a,a,z\right)=e^{z}}}$	`KummerM(a, a, z)= exp(z)`	`Hypergeometric1F1[a, a, z]= Exp[z]`	Successful	Successful	-	-
13.6.E2	${\displaystyle{\displaystyle M\left(1,2,2z\right)=\frac{e^{z}}{z}\sinh z}}$	`KummerM(1, 2, 2z)=(exp(z))/(z)sinh(z)`	`Hypergeometric1F1[1, 2, 2z]=Divide[Exp[z],z]Sinh[z]`	Successful	Successful	-	-
13.6.E3	${\displaystyle{\displaystyle M\left(0,b,z\right)=U\left(0,b,z\right)}}$	`KummerM(0, b, z)= KummerU(0, b, z)`	`Hypergeometric1F1[0, b, z]= HypergeometricU[0, b, z]`	Successful	Successful	-	-
13.6.E3	${\displaystyle{\displaystyle U\left(0,b,z\right)=1}}$	`KummerU(0, b, z)= 1`	`HypergeometricU[0, b, z]= 1`	Successful	Successful	-	-
13.6.E4	${\displaystyle{\displaystyle U\left(a,a+1,z\right)=z^{-a}}}$	`KummerU(a, a + 1, z)= (z)^(- a)`	`HypergeometricU[a, a + 1, z]= (z)^(- a)`	Failure	Successful	Successful	-
13.6.E5	${\displaystyle{\displaystyle M\left(a,a+1,-z\right)=e^{-z}M\left(1,a+1,z\right% )}}$	`KummerM(a, a + 1, - z)= exp(- z)*KummerM(1, a + 1, z)`	`Hypergeometric1F1[a, a + 1, - z]= Exp[- z]*Hypergeometric1F1[1, a + 1, z]`	Successful	Successful	-	-
13.6.E5	${\displaystyle{\displaystyle e^{-z}M\left(1,a+1,z\right)=az^{-a}\gamma\left(a,% z\right)}}$	`exp(- z)KummerM(1, a + 1, z)= a(z)^(- a)* GAMMA(a)-GAMMA(a, z)`	`Exp[- z]Hypergeometric1F1[1, a + 1, z]= a(z)^(- a)* Gamma[a, 0, z]`	Failure	Successful	Fail `-.577162386e-1+.3563618752I <- {a = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.4492199205+.4890257481I <- {a = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `21.39901789+84.08885044I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `10.80783636-3.379514632I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	-
13.6.E6	${\displaystyle{\displaystyle U\left(a,a,z\right)=z^{1-a}U\left(1,2-a,z\right)}}$	`KummerU(a, a, z)= (z)^(1 - a)* KummerU(1, 2 - a, z)`	`HypergeometricU[a, a, z]= (z)^(1 - a)* HypergeometricU[1, 2 - a, z]`	Successful	Successful	-	-
13.6.E6	${\displaystyle{\displaystyle z^{1-a}U\left(1,2-a,z\right)=z^{1-a}e^{z}E_{a}% \left(z\right)}}$	`(z)^(1 - a)* KummerU(1, 2 - a, z)= (z)^(1 - a)* exp(z)*Ei(a, z)`	`(z)^(1 - a)* HypergeometricU[1, 2 - a, z]= (z)^(1 - a)* Exp[z]*ExpIntegralE[a, z]`	Successful	Successful	-	-
13.6.E6	${\displaystyle{\displaystyle z^{1-a}e^{z}E_{a}\left(z\right)=e^{z}\Gamma\left(% 1-a,z\right)}}$	`(z)^(1 - a)* exp(z)Ei(a, z)= exp(z)GAMMA(1 - a, z)`	`(z)^(1 - a)* Exp[z]ExpIntegralE[a, z]= Exp[z]Gamma[1 - a, z]`	Successful	Successful	-	-
13.6.E7	${\displaystyle{\displaystyle M\left(\tfrac{1}{2},\tfrac{3}{2},-z^{2}\right)=% \frac{\sqrt{\pi}}{2z}\operatorname{erf}\left(z\right)}}$	`KummerM((1)/(2), (3)/(2), - (z)^(2))=(sqrt(Pi))/(2z)erf(z)`	`Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)]=Divide[Sqrt[Pi],2z]Erf[z]`	Successful	Successful	-	-
13.6.E8	${\displaystyle{\displaystyle U\left(\tfrac{1}{2},\tfrac{1}{2},z^{2}\right)=% \sqrt{\pi}e^{z^{2}}\operatorname{erfc}\left(z\right)}}$	`KummerU((1)/(2), (1)/(2), (z)^(2))=sqrt(Pi)exp((z)^(2))erfc(z)`	`HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)]=Sqrt[Pi]Exp[(z)^(2)]Erfc[z]`	Failure	Failure	Fail `3.075886301+2.075744094I <- {z = -2^(1/2)-I2^(1/2)}` `3.075886301-2.075744094I <- {z = -2^(1/2)+I2^(1/2)}`	Fail `Complex[3.0758862951142576, 2.0757440991874905] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.0758862951142576, -2.0757440991874905] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.6.E9	${\displaystyle{\displaystyle M\left(\nu+\tfrac{1}{2},2\nu+1,2z\right)=\Gamma% \left(1+\nu\right)e^{z}\left(\ifrac{z}{2}\right)^{-\nu}I_{\nu}\left(z\right)}}$	`KummerM(nu +(1)/(2), 2nu + 1, 2z)= GAMMA(1 + nu)exp(z)((z)/(2))^(- nu)* BesselI(nu, z)`	`Hypergeometric1F1[\[Nu]+Divide[1,2], 2\[Nu]+ 1, 2z]= Gamma[1 + \[Nu]]Exp[z](Divide[z,2])^(- \[Nu])* BesselI[\[Nu], z]`	Successful	Successful	-	-
13.6.E10	${\displaystyle{\displaystyle U\left(\nu+\tfrac{1}{2},2\nu+1,2z\right)=\frac{1}% {\sqrt{\pi}}e^{z}\left(2z\right)^{-\nu}K_{\nu}\left(z\right)}}$	`KummerU(nu +(1)/(2), 2nu + 1, 2z)=(1)/(sqrt(Pi))exp(z)(2z)^(- nu) BesselK(nu, z)`	`HypergeometricU[\[Nu]+Divide[1,2], 2\[Nu]+ 1, 2z]=Divide[1,Sqrt[Pi]]Exp[z](2z)^(- \[Nu]) BesselK[\[Nu], z]`	Successful	Successful	-	-
13.6.E11	${\displaystyle{\displaystyle U\left(\tfrac{5}{6},\tfrac{5}{3},\tfrac{4}{3}z^{3% /2}\right)=\sqrt{\pi}\frac{3^{5/6}\exp\left(\tfrac{2}{3}z^{3/2}\right)}{2^{2/3% }z}\mathrm{Ai}\left(z\right)}}$	`KummerU((5)/(6), (5)/(3), (4)/(3)(z)^(3/ 2))=sqrt(Pi)((3)^(5/ 6)* exp((2)/(3)(z)^(3/ 2)))/((2)^(2/ 3) z)*AiryAi(z)`	`HypergeometricU[Divide[5,6], Divide[5,3], Divide[4,3](z)^(3/ 2)]=Sqrt[Pi]Divide[(3)^(5/ 6)* Exp[Divide[2,3](z)^(3/ 2)],(2)^(2/ 3) z]*AiryAi[z]`	Failure	Failure	Fail `.1287113381-.3250284300I <- {z = -2^(1/2)-I2^(1/2)}` `.1287113381+.3250284300I <- {z = -2^(1/2)+I2^(1/2)}`	Fail `Complex[0.12871133806471044, -0.32502842978110724] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.12871133806471044, 0.32502842978110724] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.6.E12	${\displaystyle{\displaystyle U\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},% \tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a+\frac{1}{4}}e^{\frac{1}{4}z^{2}}U% \left(a,z\right)}}$	`KummerU((1)/(2)a +(1)/(4), (1)/(2), (1)/(2)(z)^(2))= (2)^((1)/(2)a +(1)/(4)) exp((1)/(4)(z)^(2))CylinderU(a, z)`	`HypergeometricU[Divide[1,2]a +Divide[1,4], Divide[1,2], Divide[1,2](z)^(2)]= (2)^(Divide[1,2]a +Divide[1,4]) Exp[Divide[1,4](z)^(2)]ParabolicCylinderD[-a - 1/2, z]`	Failure	Failure	Fail `5.265954080+2.598925556I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `16.95026320+24.47160682I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `16.95026320-24.47160682I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `5.265954080-2.598925556I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[5.265954078844872, 2.598925568096585] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[16.95026324285485, 24.471606828175403] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[16.95026324285485, -24.471606828175403] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.265954078844872, -2.598925568096585] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.6.E13	${\displaystyle{\displaystyle U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},% \tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}% }}{z}U\left(a,z\right)}}$	`KummerU((1)/(2)a +(3)/(4), (3)/(2), (1)/(2)(z)^(2))= (2)^((1)/(2)a +(3)/(4))(exp((1)/(4)(z)^(2)))/(z)CylinderU(a, z)`	`HypergeometricU[Divide[1,2]a +Divide[3,4], Divide[3,2], Divide[1,2](z)^(2)]= (2)^(Divide[1,2]a +Divide[3,4])Divide[Exp[Divide[1,4](z)^(2)],z]ParabolicCylinderD[-a - 1/2, z]`	Failure	Failure	Fail `-4.996298330+.8383991143I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `3.915433252-20.40791018I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `3.915433252+20.40791018I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-4.996298330-.8383991143I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[-4.996298332347829, 0.8383991090064162] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[3.9154332288113323, -20.407910193592727] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[3.9154332288113323, 20.407910193592727] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.996298332347829, -0.8383991090064162] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.6.E14	${\displaystyle{\displaystyle M\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},% \tfrac{1}{2}z^{2}\right)=\frac{2^{\frac{1}{2}a-\frac{3}{4}}\Gamma\left(\tfrac{% 1}{2}a+\tfrac{3}{4}\right)e^{\frac{1}{4}z^{2}}}{\sqrt{\pi}}\*\left(U\left(a,z% \right)+U\left(a,-z\right)\right)}}$	`KummerM((1)/(2)a +(1)/(4), (1)/(2), (1)/(2)(z)^(2))=((2)^((1)/(2)a -(3)/(4)) GAMMA((1)/(2)a +(3)/(4))exp((1)/(4)(z)^(2)))/(sqrt(Pi))(CylinderU(a, z)+ CylinderU(a, - z))`	`Hypergeometric1F1[Divide[1,2]a +Divide[1,4], Divide[1,2], Divide[1,2](z)^(2)]=Divide[(2)^(Divide[1,2]a -Divide[3,4]) Gamma[Divide[1,2]a +Divide[3,4]]Exp[Divide[1,4](z)^(2)],Sqrt[Pi]](ParabolicCylinderD[-a - 1/2, z]+ ParabolicCylinderD[-a - 1/2, - z])`	Successful	Successful	-	-
13.6.E15	${\displaystyle{\displaystyle M\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},% \tfrac{1}{2}z^{2}\right)=\frac{2^{\frac{1}{2}a-\frac{5}{4}}\Gamma\left(\tfrac{% 1}{2}a+\tfrac{1}{4}\right)e^{\frac{1}{4}z^{2}}}{z\sqrt{\pi}}\*\left(U\left(a,-% z\right)-U\left(a,z\right)\right)}}$	`KummerM((1)/(2)a +(3)/(4), (3)/(2), (1)/(2)(z)^(2))=((2)^((1)/(2)a -(5)/(4)) GAMMA((1)/(2)a +(1)/(4))exp((1)/(4)(z)^(2)))/(zsqrt(Pi))*(CylinderU(a, - z)- CylinderU(a, z))`	`Hypergeometric1F1[Divide[1,2]a +Divide[3,4], Divide[3,2], Divide[1,2](z)^(2)]=Divide[(2)^(Divide[1,2]a -Divide[5,4]) Gamma[Divide[1,2]a +Divide[1,4]]Exp[Divide[1,4](z)^(2)],zSqrt[Pi]]*(ParabolicCylinderD[-a - 1/2, - z]- ParabolicCylinderD[-a - 1/2, z])`	Successful	Successful	-	-
13.6.E16	${\displaystyle{\displaystyle M\left(-n,\tfrac{1}{2},z^{2}\right)=(-1)^{n}\frac% {n!}{(2n)!}H_{2n}\left(z\right)}}$	`KummerM(- n, (1)/(2), (z)^(2))=(- 1)^(n)(factorial(n))/(factorial(2n))HermiteH(2n, z)`	`Hypergeometric1F1[- n, Divide[1,2], (z)^(2)]=(- 1)^(n)Divide[(n)!,(2n)!]HermiteH[2n, z]`	Failure	Failure	Successful	Successful
13.6.E17	${\displaystyle{\displaystyle M\left(-n,\tfrac{3}{2},z^{2}\right)=(-1)^{n}\frac% {n!}{(2n+1)!2z}H_{2n+1}\left(z\right)}}$	`KummerM(- n, (3)/(2), (z)^(2))=(- 1)^(n)(factorial(n))/(factorial(2n + 1)2z)HermiteH(2n + 1, z)`	`Hypergeometric1F1[- n, Divide[3,2], (z)^(2)]=(- 1)^(n)Divide[(n)!,(2n + 1)!2z]HermiteH[2n + 1, z]`	Failure	Failure	Successful	Successful
13.6.E18	${\displaystyle{\displaystyle U\left(\tfrac{1}{2}-\tfrac{1}{2}n,\tfrac{3}{2},z^% {2}\right)=2^{-n}z^{-1}H_{n}\left(z\right)}}$	`KummerU((1)/(2)-(1)/(2)n, (3)/(2), (z)^(2))= (2)^(- n) (z)^(- 1)* HermiteH(n, z)`	`HypergeometricU[Divide[1,2]-Divide[1,2]n, Divide[3,2], (z)^(2)]= (2)^(- n) (z)^(- 1)* HermiteH[n, z]`	Failure	Failure	Fail `2.474873733+3.181980514I <- {z = -2^(1/2)-I2^(1/2), n = 2}` `2.474873733-3.181980514I <- {z = -2^(1/2)+I2^(1/2), n = 2}`	Fail `Complex[2.4748737341529163, 3.181980515339464] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.474873734152916, -3.181980515339464] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.6.E19	${\displaystyle{\displaystyle U\left(-n,\alpha+1,z\right)=(-1)^{n}{\left(\alpha% +1\right)_{n}}M\left(-n,\alpha+1,z\right)}}$	`KummerU(- n, alpha + 1, z)=(- 1)^(n)* pochhammer(alpha + 1, n)*KummerM(- n, alpha + 1, z)`	`HypergeometricU[- n, \[Alpha]+ 1, z]=(- 1)^(n)* Pochhammer[\[Alpha]+ 1, n]*Hypergeometric1F1[- n, \[Alpha]+ 1, z]`	Failure	Failure	Successful	Successful
13.6.E20	${\displaystyle{\displaystyle U\left(-n,z-n+1,a\right)={\left(-z\right)_{n}}M% \left(-n,z-n+1,a\right)}}$	`KummerU(- n, z - n + 1, a)= pochhammer(- z, n)*KummerM(- n, z - n + 1, a)`	`HypergeometricU[- n, z - n + 1, a]= Pochhammer[- z, n]*Hypergeometric1F1[- n, z - n + 1, a]`	Failure	Failure	Skip	Successful
13.6.E21	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}{{}_{2}F_{0}}\left(a,a-% b+1;-;-z^{-1}\right)}}$	`KummerU(a, b, z)= (z)^(- a)* hypergeom([a , a - b + 1], [-], - (z)^(- 1))`	`HypergeometricU[a, b, z]= (z)^(- a)* HypergeometricPFQ[{a , a - b + 1}, {-}, - (z)^(- 1)]`	Error	Failure	-	Error
13.7.E4	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{% \left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s}+\varepsilon_{n}(z)}}$	`KummerU(a, b, z)= (z)^(- a)* sum((pochhammer(a, s)pochhammer(a - b + 1, s))/(factorial(s))(- z)^(- s), s = 0..n - 1)+ varepsilon[n]*(z)`	`HypergeometricU[a, b, z]= (z)^(- a)* Sum[Divide[Pochhammer[a, s]Pochhammer[a - b + 1, s],(s)!](- z)^(- s), {s, 0, n - 1}]+ Subscript[\[CurlyEpsilon], n]*(z)`	Failure	Failure	Skip	Skip
13.7#Ex3	${\displaystyle{\displaystyle\chi(n)=\sqrt{\pi}\Gamma\left(\tfrac{1}{2}n+1% \right)/\Gamma\left(\tfrac{1}{2}n+\tfrac{1}{2}\right)}}$	`chi(n)=sqrt(Pi)GAMMA((1)/(2)n + 1)/ GAMMA((1)/(2)n +(1)/(2))`	`\[Chi](n)=Sqrt[Pi]Gamma[Divide[1,2]n + 1]/ Gamma[Divide[1,2]n +Divide[1,2]]`	Failure	Failure	Fail `-.156582765+1.414213562I <- {chi = 2^(1/2)+I2^(1/2), n = 1}` `.828427124+2.828427124I <- {chi = 2^(1/2)+I2^(1/2), n = 2}` `1.886446196+4.242640686I <- {chi = 2^(1/2)+I2^(1/2), n = 3}` `-.156582765-1.414213562I <- {chi = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Fail `Complex[-0.1565827644218014, 1.4142135623730951] <- {Rule[n, 1], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[0.8284271247461903, 2.8284271247461903] <- {Rule[n, 2], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[1.8864461969269408, 4.242640687119286] <- {Rule[n, 3], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-0.1565827644218014, -1.4142135623730951] <- {Rule[n, 1], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.7.E10	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{% \left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s}+R_{n}(a,b,z)}}$	`KummerU(a, b, z)= (z)^(- a)* sum((pochhammer(a, s)pochhammer(a - b + 1, s))/(factorial(s))(- z)^(- s), s = 0..n - 1)+ R[n]*(a , b , z)`	`HypergeometricU[a, b, z]= (z)^(- a)* Sum[Divide[Pochhammer[a, s]Pochhammer[a - b + 1, s],(s)!](- z)^(- s), {s, 0, n - 1}]+ Subscript[R, n]*(a , b , z)`	Failure	Failure	Skip	Error
13.8.E3	${\displaystyle{\displaystyle\left(e^{t}-1\right)^{a-1}\exp\left(t+z(1-e^{-t})% \right)=\sum_{s=0}^{\infty}q_{s}(z,a)t^{s+a-1}}}$	`(exp(t)- 1)^(a - 1)* exp(t + z(1 - exp(- t)))= sum(q[s](z , a)* (t)^(s + a - 1), s = 0..infinity)`	`(Exp[t]- 1)^(a - 1)* Exp[t + z(1 - Exp[- t])]= Sum[Subscript[q, s](z , a)* (t)^(s + a - 1), {s, 0, Infinity}]`	Error	Failure	-	Error
13.8#Ex1	${\displaystyle{\displaystyle p_{k}(z)=\sum_{s=0}^{k}\genfrac{(}{)}{0.0pt}{}{k}% {s}{\left(1-b+s\right)_{k-s}}z^{s}c_{k+s}(z)}}$	`p[k](z)= sum(binomial(k,s)pochhammer(1 - b + s, k - s)(z)^(s) c[k + s]*(z), s = 0..k)`	`Subscript[p, k](z)= Sum[Binomial[k,s]Pochhammer[1 - b + s, k - s](z)^(s) Subscript[c, k + s]*(z), {s, 0, k}]`	Failure	Failure	Skip	Skip
13.8#Ex2	${\displaystyle{\displaystyle q_{k}(z)=\sum_{s=0}^{k}\genfrac{(}{)}{0.0pt}{}{k}% {s}{\left(2-b+s\right)_{k-s}}z^{s}c_{k+s+1}(z)}}$	`q[k](z)= sum(binomial(k,s)pochhammer(2 - b + s, k - s)(z)^(s) c[k + s + 1]*(z), s = 0..k)`	`Subscript[q, k](z)= Sum[Binomial[k,s]Pochhammer[2 - b + s, k - s](z)^(s) Subscript[c, k + s + 1]*(z), {s, 0, k}]`	Failure	Failure	Skip	Skip
13.8.E16	${\displaystyle{\displaystyle(k+1)c_{k+1}(z)+\sum_{s=0}^{k}\left(\frac{bB_{s+1}% }{(s+1)!}+\frac{z(s+1)B_{s+2}}{(s+2)!}\right)c_{k-s}(z)=0}}$	`(k + 1)* c[k + 1](z)+ sum(((bbernoulli(s + 1))/(factorial(s + 1))+(z(s + 1) bernoulli(s + 2))/(factorial(s + 2)))* c[k - s]*(z), s = 0..k)= 0`	`(k + 1)* Subscript[c, k + 1](z)+ Sum[(Divide[bBernoulliB[s + 1],(s + 1)!]+Divide[z(s + 1) BernoulliB[s + 2],(s + 2)!])* Subscript[c, k - s]*(z), {s, 0, k}]= 0`	Failure	Failure	Skip	Successful
13.8#Ex3	${\displaystyle{\displaystyle\frac{\partial f}{\partial t}=\left(b\left(\frac{1% }{t}-\frac{1}{e^{t}-1}\right)-z\left(\frac{1}{t^{2}}-\frac{e^{t}}{\left(e^{t}-% 1\right)^{2}}\right)\right)f}}$	`diff(f, t)=(b((1)/(t)-(1)/(exp(t)- 1))- z((1)/((t)^(2))-(exp(t))/((exp(t)- 1)^(2))))* f`	`D[f, t]=(b(Divide[1,t]-Divide[1,Exp[t]- 1])- z(Divide[1,(t)^(2)]-Divide[Exp[t],(Exp[t]- 1)^(2)]))* f`	Failure	Failure	Fail `-.3721020438-1.177486994I <- {b = 2^(1/2)+I2^(1/2), f = 2^(1/2)+I2^(1/2), t = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.1143697985-1.565636569I <- {b = 2^(1/2)+I2^(1/2), f = 2^(1/2)+I2^(1/2), t = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-.5025193734-1.823368814I <- {b = 2^(1/2)+I2^(1/2), f = 2^(1/2)+I2^(1/2), t = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-.7602516187-1.435219239I <- {b = 2^(1/2)+I2^(1/2), f = 2^(1/2)+I2^(1/2), t = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Skip
13.9.E1	${\displaystyle{\displaystyle p(a,b)=\left\lceil-a\right\rceil}}$	`p*(a , b)= ceil(- a)`	`p*(a , b)= Ceiling[- a]`	Failure	Failure	Error	Error
13.9.E4	${\displaystyle{\displaystyle p(a,b)=\left\lfloor-\tfrac{1}{2}b\right\rfloor-% \left\lfloor-\tfrac{1}{2}(b+1)\right\rfloor}}$	`p(a , b)= floor(-(1)/(2)b)- floor(-(1)/(2)*(b + 1))`	`p(a , b)= Floor[-Divide[1,2]b]- Floor[-Divide[1,2]*(b + 1)]`	Failure	Failure	Error	Error
13.9.E5	${\displaystyle{\displaystyle p(a,b)=\left\lceil-a\right\rceil-\left\lceil-b% \right\rceil}}$	`p*(a , b)= ceil(- a)- ceil(- b)`	`p*(a , b)= Ceiling[- a]- Ceiling[- b]`	Failure	Failure	Skip	Error
13.9.E6	${\displaystyle{\displaystyle p(a,b)=\left\lfloor\tfrac{1}{2}\left(\left\lceil-% b\right\rceil-\left\lceil-a\right\rceil+1\right)\right\rfloor-\left\lfloor% \tfrac{1}{2}\left(\left\lceil-b\right\rceil-\left\lceil-a\right\rceil\right)% \right\rfloor}}$	`p(a , b)= floor((1)/(2)(ceil(- b)- ceil(- a)+ 1))- floor((1)/(2)*(ceil(- b)- ceil(- a)))`	`p(a , b)= Floor[Divide[1,2](Ceiling[- b]- Ceiling[- a]+ 1)]- Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a])]`	Failure	Failure	Skip	Error
13.9.E11	${\displaystyle{\displaystyle T(a,b)=\left\lfloor-a\right\rfloor+1}}$	`T*(a , b)= floor(- a)+ 1`	`T*(a , b)= Floor[- a]+ 1`	Error	Failure	-	Error
13.9.E12	${\displaystyle{\displaystyle T(a,b)=\left\lfloor-a\right\rfloor}}$	`T*(a , b)= floor(- a)`	`T*(a , b)= Floor[- a]`	Error	Failure	-	Error
13.9.E14	${\displaystyle{\displaystyle P(a,b)=\left\lceil b-a-1\right\rceil}}$	`P*(a , b)= ceil(b - a - 1)`	`P*(a , b)= Ceiling[b - a - 1]`	Failure	Failure	Skip	Error
13.10.E1	${\displaystyle{\displaystyle\int{\mathbf{M}}\left(a,b,z\right)\mathrm{d}z=% \frac{1}{a-1}{\mathbf{M}}\left(a-1,b-1,z\right)}}$	`int(KummerM(a, b, z)/GAMMA(b), z)=(1)/(a - 1)*KummerM(a - 1, b - 1, z)/GAMMA(b - 1)`	`Integrate[Hypergeometric1F1Regularized[a, b, z], z]=Divide[1,a - 1]*Hypergeometric1F1Regularized[a - 1, b - 1, z]`	Successful	Failure	-	Skip
13.10.E2	${\displaystyle{\displaystyle\int U\left(a,b,z\right)\mathrm{d}z=-\frac{1}{a-1}% U\left(a-1,b-1,z\right)}}$	`int(KummerU(a, b, z), z)= -(1)/(a - 1)*KummerU(a - 1, b - 1, z)`	`Integrate[HypergeometricU[a, b, z], z]= -Divide[1,a - 1]*HypergeometricU[a - 1, b - 1, z]`	Successful	Successful	-	-
13.10.E3	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{b-1}{\mathbf{M}}\left(a% ,c,kt\right)\mathrm{d}t=\Gamma\left(b\right)z^{-b}{{}_{2}{\mathbf{F}}_{1}}% \left(a,b;c;\ifrac{k}{z}\right)}}$	`int(exp(- zt)(t)^(b - 1)* KummerM(a, c, kt)/GAMMA(c), t = 0..infinity)= GAMMA(b)(z)^(- b)* hypergeom([a , b], [c], (k)/(z))`	`Integrate[Exp[- zt](t)^(b - 1)* Hypergeometric1F1Regularized[a, c, kt], {t, 0, Infinity}]= Gamma[b](z)^(- b)* HypergeometricPFQRegularized[{a , b}, {c}, Divide[k,z]]`	Failure	Failure	Skip	Error
13.10.E4	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{b-1}{\mathbf{M}}\left(a% ,b,t\right)\mathrm{d}t=z^{-b}\left(1-\frac{1}{z}\right)^{-a}}}$	`int(exp(- zt)(t)^(b - 1)* KummerM(a, b, t)/GAMMA(b), t = 0..infinity)= (z)^(- b)*(1 -(1)/(z))^(- a)`	`Integrate[Exp[- zt](t)^(b - 1)* Hypergeometric1F1Regularized[a, b, t], {t, 0, Infinity}]= (z)^(- b)*(1 -Divide[1,z])^(- a)`	Failure	Failure	Skip	Error
13.10.E5	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-t}t^{b-1}{\mathbf{M}}\left(a,% c,t\right)\mathrm{d}t=\frac{\Gamma\left(b\right)\Gamma\left(c-a-b\right)}{% \Gamma\left(c-a\right)\Gamma\left(c-b\right)}}}$	`int(exp(- t)(t)^(b - 1) KummerM(a, c, t)/GAMMA(c), t = 0..infinity)=(GAMMA(b)GAMMA(c - a - b))/(GAMMA(c - a)GAMMA(c - b))`	`Integrate[Exp[- t](t)^(b - 1) Hypergeometric1F1Regularized[a, c, t], {t, 0, Infinity}]=Divide[Gamma[b]Gamma[c - a - b],Gamma[c - a]Gamma[c - b]]`	Failure	Failure	Skip	Error
13.10.E6	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt-t^{2}}t^{2b-2}{\mathbf{M}}% \left(a,b,t^{2}\right)\mathrm{d}t=\tfrac{1}{2}\pi^{-\frac{1}{2}}\Gamma\left(b-% \tfrac{1}{2}\right)U\left(b-\tfrac{1}{2},a+\tfrac{1}{2},\tfrac{1}{4}z^{2}% \right)}}$	`int(exp(- zt - (t)^(2))(t)^(2b - 2) KummerM(a, b, (t)^(2))/GAMMA(b), t = 0..infinity)=(1)/(2)(Pi)^(-(1)/(2)) GAMMA(b -(1)/(2))KummerU(b -(1)/(2), a +(1)/(2), (1)/(4)(z)^(2))`	`Integrate[Exp[- zt - (t)^(2)](t)^(2b - 2) Hypergeometric1F1Regularized[a, b, (t)^(2)], {t, 0, Infinity}]=Divide[1,2](Pi)^(-Divide[1,2]) Gamma[b -Divide[1,2]]HypergeometricU[b -Divide[1,2], a +Divide[1,2], Divide[1,4](z)^(2)]`	Failure	Failure	Skip	Error
13.10.E7	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{b-1}U\left(a,c,t\right)% \mathrm{d}t=\Gamma\left(b\right)\Gamma\left(b-c+1\right)\*z^{-b}{{}_{2}{% \mathbf{F}}_{1}}\left(a,b;a+b-c+1;1-\frac{1}{z}\right)}}$	`int(exp(- zt)(t)^(b - 1)* KummerU(a, c, t), t = 0..infinity)= GAMMA(b)GAMMA(b - c + 1) (z)^(- b)* hypergeom([a , b], [a + b - c + 1], 1 -(1)/(z))`	`Integrate[Exp[- zt](t)^(b - 1)* HypergeometricU[a, c, t], {t, 0, Infinity}]= Gamma[b]Gamma[b - c + 1] (z)^(- b)* HypergeometricPFQRegularized[{a , b}, {a + b - c + 1}, 1 -Divide[1,z]]`	Failure	Failure	Skip	Error
13.10.E8	${\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e^{tz% }t^{-a}{\mathbf{M}}\left(a,b,\ifrac{y}{t}\right)\mathrm{d}t=\frac{1}{\Gamma% \left(a\right)}z^{\frac{1}{2}(2a-b-1)}y^{\frac{1}{2}(1-b)}I_{b-1}\left(2\sqrt{% zy}\right)}}$	`(1)/(2PiI)int(exp(tz)(t)^(- a) KummerM(a, b, (y)/(t))/GAMMA(b), t = - infinity..(0 +))=(1)/(GAMMA(a))(z)^((1)/(2)(2a - b - 1)) (y)^((1)/(2)(1 - b)) BesselI(b - 1, 2sqrt(zy))`	`Divide[1,2PiI]Integrate[Exp[tz](t)^(- a) Hypergeometric1F1Regularized[a, b, Divide[y,t]], {t, - Infinity, (0 +)}]=Divide[1,Gamma[a]](z)^(Divide[1,2](2a - b - 1)) (y)^(Divide[1,2](1 - b)) BesselI[b - 1, 2Sqrt[zy]]`	Error	Failure	-	Error
13.10.E9	${\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e^{tz% }t^{-a}U\left(a,b,\ifrac{y}{t}\right)\mathrm{d}t=\frac{2z^{\frac{1}{2}(2a-b-1)% }y^{\frac{1}{2}(1-b)}}{\Gamma\left(a\right)\Gamma\left(a-b+1\right)}K_{b-1}% \left(2\sqrt{zy}\right)}}$	`(1)/(2PiI)int(exp(tz)(t)^(- a) KummerU(a, b, (y)/(t)), t = - infinity..(0 +))=(2(z)^((1)/(2)(2a - b - 1)) (y)^((1)/(2)(1 - b)))/(GAMMA(a)GAMMA(a - b + 1))BesselK(b - 1, 2sqrt(z*y))`	`Divide[1,2PiI]Integrate[Exp[tz](t)^(- a) HypergeometricU[a, b, Divide[y,t]], {t, - Infinity, (0 +)}]=Divide[2(z)^(Divide[1,2](2a - b - 1)) (y)^(Divide[1,2](1 - b)),Gamma[a]Gamma[a - b + 1]]BesselK[b - 1, 2Sqrt[z*y]]`	Error	Failure	-	Error
13.10.E10	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\lambda-1}{\mathbf{M}}\left(a,% b,-t\right)\mathrm{d}t=\frac{\Gamma\left(\lambda\right)\Gamma\left(a-\lambda% \right)}{\Gamma\left(a\right)\Gamma\left(b-\lambda\right)}}}$	`int((t)^(lambda - 1)* KummerM(a, b, - t)/GAMMA(b), t = 0..infinity)=(GAMMA(lambda)GAMMA(a - lambda))/(GAMMA(a)GAMMA(b - lambda))`	`Integrate[(t)^(\[Lambda]- 1)* Hypergeometric1F1Regularized[a, b, - t], {t, 0, Infinity}]=Divide[Gamma[\[Lambda]]Gamma[a - \[Lambda]],Gamma[a]Gamma[b - \[Lambda]]]`	Successful	Failure	-	Error
13.10.E11	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\lambda-1}U\left(a,b,t\right)% \mathrm{d}t=\frac{\Gamma\left(\lambda\right)\Gamma\left(a-\lambda\right)\Gamma% \left(\lambda-b+1\right)}{\Gamma\left(a\right)\Gamma\left(a-b+1\right)}}}$	`int((t)^(lambda - 1)* KummerU(a, b, t), t = 0..infinity)=(GAMMA(lambda)GAMMA(a - lambda)GAMMA(lambda - b + 1))/(GAMMA(a)*GAMMA(a - b + 1))`	`Integrate[(t)^(\[Lambda]- 1)* HypergeometricU[a, b, t], {t, 0, Infinity}]=Divide[Gamma[\[Lambda]]Gamma[a - \[Lambda]]Gamma[\[Lambda]- b + 1],Gamma[a]*Gamma[a - b + 1]]`	Successful	Failure	-	Error
13.10.E12	${\displaystyle{\displaystyle\int_{0}^{\infty}\cos\left(2xt\right){\mathbf{M}}% \left(a,b,-t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}}{2\Gamma\left(a\right)}x^{% 2a-1}e^{-x^{2}}U\left(b-\tfrac{1}{2},a+\tfrac{1}{2},x^{2}\right)}}$	`int(cos(2xt)KummerM(a, b, - (t)^(2))/GAMMA(b), t = 0..infinity)=(sqrt(Pi))/(2GAMMA(a))(x)^(2a - 1)* exp(- (x)^(2))*KummerU(b -(1)/(2), a +(1)/(2), (x)^(2))`	`Integrate[Cos[2xt]Hypergeometric1F1Regularized[a, b, - (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi],2Gamma[a]](x)^(2a - 1)* Exp[- (x)^(2)]*HypergeometricU[b -Divide[1,2], a +Divide[1,2], (x)^(2)]`	Failure	Failure	Skip	Error
13.10.E13	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-t}t^{b-1-\frac{1}{2}\nu}{% \mathbf{M}}\left(a,b,t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=x^{-a+% \frac{1}{2}\nu}e^{-x}{\mathbf{M}}\left(\nu-b+1,\nu-a+1,x\right)}}$	`int(exp(- t)(t)^(b - 1 -(1)/(2)nu)* KummerM(a, b, t)/GAMMA(b)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)= (x)^(- a +(1)/(2)nu)* exp(- x)*KummerM(nu - b + 1, nu - a + 1, x)/GAMMA(nu - a + 1)`	`Integrate[Exp[- t](t)^(b - 1 -Divide[1,2]\[Nu])* Hypergeometric1F1Regularized[a, b, t]BesselJ[\[Nu], 2Sqrt[xt]], {t, 0, Infinity}]= (x)^(- a +Divide[1,2]\[Nu])* Exp[- x]*Hypergeometric1F1Regularized[\[Nu]- b + 1, \[Nu]- a + 1, x]`	Failure	Failure	Skip	Error
13.10.E14	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}\nu}{\mathbf{% M}}\left(a,b,t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{x^{\frac{% 1}{2}\nu}e^{-x}}{\Gamma\left(b-a\right)}U\left(a,a-b+\nu+2,x\right)}}$	`int(exp(- t)(t)^((1)/(2)nu)* KummerM(a, b, t)/GAMMA(b)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)=((x)^((1)/(2)nu)* exp(- x))/(GAMMA(b - a))*KummerU(a, a - b + nu + 2, x)`	`Integrate[Exp[- t](t)^(Divide[1,2]\[Nu])* Hypergeometric1F1Regularized[a, b, t]BesselJ[\[Nu], 2Sqrt[xt]], {t, 0, Infinity}]=Divide[(x)^(Divide[1,2]\[Nu])* Exp[- x],Gamma[b - a]]*HypergeometricU[a, a - b + \[Nu]+ 2, x]`	Failure	Failure	Skip	Error
13.10.E15	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\frac{1}{2}\nu}U\left(a,b,t% \right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{\Gamma\left(\nu-b+2% \right)}{\Gamma\left(a\right)}x^{\frac{1}{2}\nu}U\left(\nu-b+2,\nu-a+2,x\right% )}}$	`int((t)^((1)/(2)nu) KummerU(a, b, t)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)=(GAMMA(nu - b + 2))/(GAMMA(a))(x)^((1)/(2)nu) KummerU(nu - b + 2, nu - a + 2, x)`	`Integrate[(t)^(Divide[1,2]\[Nu]) HypergeometricU[a, b, t]BesselJ[\[Nu], 2Sqrt[xt]], {t, 0, Infinity}]=Divide[Gamma[\[Nu]- b + 2],Gamma[a]](x)^(Divide[1,2]\[Nu]) HypergeometricU[\[Nu]- b + 2, \[Nu]- a + 2, x]`	Failure	Failure	Skip	Error
13.10.E16	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}\nu}U\left(a,% b,t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\Gamma\left(\nu-b+2\right)% x^{\frac{1}{2}\nu}e^{-x}{\mathbf{M}}\left(a,a-b+\nu+2,x\right)}}$	`int(exp(- t)(t)^((1)/(2)nu)* KummerU(a, b, t)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)= GAMMA(nu - b + 2)(x)^((1)/(2)nu) exp(- x)*KummerM(a, a - b + nu + 2, x)/GAMMA(a - b + nu + 2)`	`Integrate[Exp[- t](t)^(Divide[1,2]\[Nu])* HypergeometricU[a, b, t]BesselJ[\[Nu], 2Sqrt[xt]], {t, 0, Infinity}]= Gamma[\[Nu]- b + 2](x)^(Divide[1,2]\[Nu]) Exp[- x]*Hypergeometric1F1Regularized[a, a - b + \[Nu]+ 2, x]`	Failure	Failure	Skip	Error
13.11.E1	${\displaystyle{\displaystyle M\left(a,b,z\right)=\Gamma\left(a-\tfrac{1}{2}% \right)e^{\frac{1}{2}z}\left(\tfrac{1}{4}z\right)^{\frac{1}{2}-a}\\sum_{s=0}^% {\infty}\frac{{\left(2a-1\right)_{s}}{\left(2a-b\right)_{s}}}{{\left(b\right)_% {s}}s!}\\left(a-\tfrac{1}{2}+s\right)\*I_{a-\frac{1}{2}+s}\left(\tfrac{1}{2}z% \right)}}$	`KummerM(a, b, z)= GAMMA(a -(1)/(2))exp((1)/(2)z)((1)/(4)z)^((1)/(2)- a)* sum((pochhammer(2a - 1, s)pochhammer(2a - b, s))/(pochhammer(b, s)factorial(s))(a -(1)/(2)+ s) BesselI(a -(1)/(2)+ s, (1)/(2)*z), s = 0..infinity)`	`Hypergeometric1F1[a, b, z]= Gamma[a -Divide[1,2]]Exp[Divide[1,2]z](Divide[1,4]z)^(Divide[1,2]- a)* Sum[Divide[Pochhammer[2a - 1, s]Pochhammer[2a - b, s],Pochhammer[b, s](s)!](a -Divide[1,2]+ s) BesselI[a -Divide[1,2]+ s, Divide[1,2]*z], {s, 0, Infinity}]`	Error	Failure	-	Skip
13.12.E1	${\displaystyle{\displaystyle M\left(a,b,z\right)M\left(-a,-b,-z\right)+\frac{a% (a-b)z^{2}}{b^{2}(1-b^{2})}M\left(1+a,2+b,z\right)M\left(1-a,2-b,-z\right)=1}}$	`KummerM(a, b, z)KummerM(- a, - b, - z)+(a(a - b)* (z)^(2))/((b)^(2)(1 - (b)^(2)))KummerM(1 + a, 2 + b, z)*KummerM(1 - a, 2 - b, - z)= 1`	`Hypergeometric1F1[a, b, z]Hypergeometric1F1[- a, - b, - z]+Divide[a(a - b)* (z)^(2),(b)^(2)(1 - (b)^(2))]Hypergeometric1F1[1 + a, 2 + b, z]*Hypergeometric1F1[1 - a, 2 - b, - z]= 1`	Failure	Failure	Successful	Skip
13.14.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}+\left(% -\frac{1}{4}+\frac{\kappa}{z}+\frac{\frac{1}{4}-\mu^{2}}{z^{2}}\right)W=0}}$	`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	Fail `-.2651650428-.4419417382I <- {W = 2^(1/2)+I2^(1/2), kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-.4419417381+2.563262081I <- {W = 2^(1/2)+I2^(1/2), kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-3.093592167-3.270368862I <- {W = 2^(1/2)+I2^(1/2), kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `2.386485386-.2651650429I <- {W = 2^(1/2)+I2^(1/2), kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[-0.2651650429449553, -0.44194173824159216] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[2.5632620818012346, 2.3864853865045976] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.2651650429449553, -0.44194173824159216] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.5632620818012346, 2.3864853865045976] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.14.E2	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \frac{1}{2}+\mu}M\left(\tfrac{1}{2}+\mu-\kappa,1+2\mu,z\right)}}$	`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	-	-
13.14.E3	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \frac{1}{2}+\mu}U\left(\tfrac{1}{2}+\mu-\kappa,1+2\mu,z\right)}}$	`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	-	-
13.14.E4	${\displaystyle{\displaystyle M\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{% 2}b}M_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right)}}$	`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	-	-
13.14.E5	${\displaystyle{\displaystyle U\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{% 2}b}W_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right)}}$	`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	-	-
13.14.E6	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_% {s}}}{{\left(1+2\mu\right)_{s}}s!}z^{s}}}$	`WhittakerM(kappa, mu, z)= exp(-(1)/(2)z)(z)^((1)/(2)+ mu)* sum((pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(1 + 2mu, 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}]`	Successful	Successful	-	-
13.14.E6	${\displaystyle{\displaystyle e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{% \infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(1+2\mu\right)_{% s}}s!}z^{s}=z^{\frac{1}{2}+\mu}\sum_{n=0}^{\infty}{{}_{2}F_{1}}\left({-n,% \tfrac{1}{2}+\mu-\kappa\atop 1+2\mu};2\right)\frac{\left(-\tfrac{1}{2}z\right)% ^{n}}{n!}}}$	`exp(-(1)/(2)z)(z)^((1)/(2)+ mu)* sum((pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(1 + 2mu, s)factorial(s))(z)^(s), s = 0..infinity)= (z)^((1)/(2)+ mu) sum(hypergeom([- n ,(1)/(2)+ mu - kappa], [1 + 2mu], 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}]= (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}]`	Failure	Failure	Skip	Skip
13.14.E7	${\displaystyle{\displaystyle\frac{{\left(-\frac{1}{2}n-\kappa\right)_{n+1}}}{(% n+1)!}M_{\kappa,\frac{1}{2}(n+1)}\left(z\right)=e^{-\frac{1}{2}z}z^{-\frac{1}{% 2}n}\sum_{s=n+1}^{\infty}\frac{{\left(-\frac{1}{2}n-\kappa\right)_{s}}}{\Gamma% \left(s-n\right)s!}z^{s}}}$	`(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}]`	Successful	Successful	-	-
13.14.E10	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{+\pi\mathrm{i}}\right)=+% \mathrm{i}e^{+\mu\pi\mathrm{i}}M_{-\kappa,\mu}\left(z\right)}}$	`WhittakerM(kappa, mu, zexp(+ PiI))= + Iexp(+ muPiI)WhittakerM(- kappa, mu, z)`	`WhittakerM[\[Kappa], \[Mu], zExp[+ PiI]]= + IExp[+ \[Mu]PiI]WhittakerM[- \[Kappa], \[Mu], z]`	Failure	Failure	Fail `-170.7233278-52.66673233I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `5.614866181-.1961391743I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-253.7484615-500.5136150I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `4338.981046-2443.697049I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[-170.7233281137989, -52.66673241325771] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-253.74846171929062, -500.51361552060405] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-27.726012706068122, -46.132000771477266] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-52.00289849528395, 25.53895774298251] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.14.E10	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{-\pi\mathrm{i}}\right)=-% \mathrm{i}e^{-\mu\pi\mathrm{i}}M_{-\kappa,\mu}\left(z\right)}}$	`WhittakerM(kappa, mu, zexp(- PiI))= - Iexp(- muPiI)WhittakerM(- kappa, mu, z)`	`WhittakerM[\[Kappa], \[Mu], zExp[- PiI]]= - IExp[- \[Mu]PiI]WhittakerM[- \[Kappa], \[Mu], z]`	Failure	Failure	Fail `-1336.329299+1299.001005I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `4031.109392-3933.985765I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-156.7833633-147.7697510I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `17.75799389-.6206610589I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` ... skip entries to safe data	Fail `Complex[-1336.3293012153467, 1299.0010073665994] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-156.7833635417097, -147.76975126580453] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-2.6144703540529446, -5.648276978861849] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[13.567482135419885, 36.936365970710575] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.14.E11	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=(% -1)^{m}e^{2m\mu\pi\mathrm{i}}M_{\kappa,\mu}\left(z\right)}}$	`WhittakerM(kappa, mu, zexp(2mPiI))=(- 1)^(m)* exp(2mmuPiI)*WhittakerM(kappa, mu, z)`	`WhittakerM[\[Kappa], \[Mu], zExp[2mPiI]]=(- 1)^(m)* Exp[2m\[Mu]PiI]*WhittakerM[\[Kappa], \[Mu], z]`	Failure	Failure	Fail `-.1992563118+.7533300151I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 1}` `-.1992264798+.7534336021I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 2}` `-.1992264621+.7534336186I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 3}` `5.614866174-.1961391695I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), m = 1}` ... skip entries to safe data	Skip
13.14.E12	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=% \frac{(-1)^{m+1}2\pi\mathrm{i}\sin\left(2\pi\mu m\right)}{\Gamma\left(\frac{1}% {2}-\mu-\kappa\right)\Gamma\left(1+2\mu\right)\sin\left(2\pi\mu\right)}M_{% \kappa,\mu}\left(z\right)+(-1)^{m}e^{-2m\mu\pi\mathrm{i}}W_{\kappa,\mu}\left(z% \right)}}$	`WhittakerW(kappa, mu, zexp(2mPiI))=((- 1)^(m + 1)* 2PiIsin(2Pimum))/(GAMMA((1)/(2)- mu - kappa)GAMMA(1 + 2mu)sin(2Pimu))WhittakerM(kappa, mu, z)+(- 1)^(m)* exp(- 2mmuPiI)*WhittakerW(kappa, mu, z)`	`WhittakerW[\[Kappa], \[Mu], zExp[2mPiI]]=Divide[(- 1)^(m + 1)* 2PiISin[2Pi\[Mu]m],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]Gamma[1 + 2\[Mu]]Sin[2Pi\[Mu]]]WhittakerM[\[Kappa], \[Mu], z]+(- 1)^(m)* Exp[- 2m\[Mu]PiI]*WhittakerW[\[Kappa], \[Mu], z]`	Failure	Failure	Fail `4888.973639-5758.546940I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 1}` `51701593.85-17588478.17I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 2}` `.3859873546e12+.827147997e11I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 3}` `339.062648-414.78030I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), m = 1}` ... skip entries to safe data	Skip
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)* WhittakerW(kappa, mu, zexp(2mPiI))= -(exp(2kappaPiI)sin(2mmuPi)+ sin((2m - 2)* muPi))/(sin(2muPi))WhittakerW(kappa, mu, z)-(sin(2mmuPi)2PiIexp(kappaPiI))/(sin(2muPi)GAMMA((1)/(2)+ mu - kappa)GAMMA((1)/(2)- mu - kappa))WhittakerW(- kappa, mu, zexp(PiI))`	`(- 1)^(m)* WhittakerW[\[Kappa], \[Mu], zExp[2mPiI]]= -Divide[Exp[2\[Kappa]PiI]Sin[2m\[Mu]Pi]+ Sin[(2m - 2)* \[Mu]Pi],Sin[2\[Mu]Pi]]WhittakerW[\[Kappa], \[Mu], z]-Divide[Sin[2m\[Mu]Pi]2PiIExp[\[Kappa]PiI],Sin[2\[Mu]Pi]Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]WhittakerW[- \[Kappa], \[Mu], zExp[PiI]]`	Failure	Failure	Fail `-.3787433625+.42488234e-1I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 1}` `9903.313865-3475.249377I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 2}` `-74336427.26-15180270.02I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), m = 3}` `-339.0626695+414.7802897I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), m = 1}` ... skip entries to safe data	Skip
13.14.E25	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),M_{% \kappa,-\mu}\left(z\right)\right\}=-2\mu}}$	`(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	Successful	Successful
13.14.E26	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{% \kappa,\mu}\left(z\right)\right\}=-\frac{\Gamma\left(1+2\mu\right)}{\Gamma% \left(\frac{1}{2}+\mu-\kappa\right)}}}$	`(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	Successful	Skip
13.14.E27	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1+2\mu% \right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{-(\frac{1}{2}+\mu)\pi% \mathrm{i}}}}$	`(WhittakerM(kappa, mu, z))diff(WhittakerW(- kappa, mu, exp(+ PiI)z), z)-diff(WhittakerM(kappa, mu, z), z)(WhittakerW(- kappa, mu, exp(+ PiI)z))=(GAMMA(1 + 2mu))/(GAMMA((1)/(2)+ mu + kappa))exp(-((1)/(2)+ mu)* Pi*I)`	`Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ PiI]z]}, z]=Divide[Gamma[1 + 2\[Mu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]Exp[-(Divide[1,2]+ \[Mu])* Pi*I]`	Failure	Failure	Fail `-139.4018328-103.8422707I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-139.4018328-103.8422707I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-34.52500080+37.00315934I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `-34.52500081+37.00315938I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E27	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1+2\mu% \right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{+(\frac{1}{2}+\mu)\pi% \mathrm{i}}}}$	`(WhittakerM(kappa, mu, z))diff(WhittakerW(- kappa, mu, exp(- PiI)z), z)-diff(WhittakerM(kappa, mu, z), z)(WhittakerW(- kappa, mu, exp(- PiI)z))=(GAMMA(1 + 2mu))/(GAMMA((1)/(2)+ mu + kappa))exp(+((1)/(2)+ mu)* Pi*I)`	`Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- PiI]z]}, z]=Divide[Gamma[1 + 2\[Mu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]Exp[+(Divide[1,2]+ \[Mu])* Pi*I]`	Failure	Failure	Fail `139.4018325+103.8422705I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `139.4018324+103.8422705I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `34.52500091-37.00315940I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `34.52500091-37.00315940I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E28	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_% {\kappa,\mu}\left(z\right)\right\}=-\frac{\Gamma\left(1-2\mu\right)}{\Gamma% \left(\frac{1}{2}-\mu-\kappa\right)}}}$	`(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	Successful	Skip
13.14.E29	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_% {-\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1-2\mu% \right)}{\Gamma\left(\frac{1}{2}-\mu+\kappa\right)}e^{-(\frac{1}{2}-\mu)\pi% \mathrm{i}}}}$	`(WhittakerM(kappa, - mu, z))diff(WhittakerW(- kappa, mu, exp(+ PiI)z), z)-diff(WhittakerM(kappa, - mu, z), z)(WhittakerW(- kappa, mu, exp(+ PiI)z))=(GAMMA(1 - 2mu))/(GAMMA((1)/(2)- mu + kappa))exp(-((1)/(2)- mu)* Pi*I)`	`Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ PiI]z]}, z]=Divide[Gamma[1 - 2\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]]]Exp[-(Divide[1,2]- \[Mu])* Pi*I]`	Failure	Failure	Fail `.3494764582e-2+.1012865874I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `.3494764522e-2+.1012865875I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `.5639963652+6.066610734I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `.5639963652+6.066610734I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E29	${\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,-\mu}\left(z\right),W_% {-\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)\right\}=\frac{\Gamma\left(1-2\mu% \right)}{\Gamma\left(\frac{1}{2}-\mu+\kappa\right)}e^{+(\frac{1}{2}-\mu)\pi% \mathrm{i}}}}$	`(WhittakerM(kappa, - mu, z))diff(WhittakerW(- kappa, mu, exp(- PiI)z), z)-diff(WhittakerM(kappa, - mu, z), z)(WhittakerW(- kappa, mu, exp(- PiI)z))=(GAMMA(1 - 2mu))/(GAMMA((1)/(2)- mu + kappa))exp(+((1)/(2)- mu)* Pi*I)`	`Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- PiI]z]}, z]=Divide[Gamma[1 - 2\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]]]Exp[+(Divide[1,2]- \[Mu])* Pi*I]`	Failure	Failure	Fail `-.3494764696e-2-.1012865889I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-.3494764619e-2-.1012865875I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-.5639963688-6.066610726I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-.5639963668-6.066610729I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E30	${\displaystyle{\displaystyle\mathscr{W}\left\{W_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{+\pi\mathrm{i}}z\right)\right\}=e^{-\kappa\pi\mathrm{i}}}}$	`(WhittakerW(kappa, mu, z))diff(WhittakerW(- kappa, mu, exp(+ PiI)z), z)-diff(WhittakerW(kappa, mu, z), z)(WhittakerW(- kappa, mu, exp(+ PiI)z))= exp(- kappaPiI)`	`Wronskian[{WhittakerW[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ PiI]z]}, z]= Exp[- \[Kappa]PiI]`	Failure	Failure	Fail `22.63381635-81.96203695I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `22.63381635-81.96203695I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `22.63381635-81.96203695I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `22.63381635-81.96203695I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E30	${\displaystyle{\displaystyle\mathscr{W}\left\{W_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{-\pi\mathrm{i}}z\right)\right\}=e^{+\kappa\pi\mathrm{i}}}}$	`(WhittakerW(kappa, mu, z))diff(WhittakerW(- kappa, mu, exp(- PiI)z), z)-diff(WhittakerW(kappa, mu, z), z)(WhittakerW(- kappa, mu, exp(- PiI)z))= exp(+ kappaPiI)`	`Wronskian[{WhittakerW[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- PiI]z]}, z]= Exp[+ \[Kappa]PiI]`	Failure	Failure	Fail `-22.63381633+81.96203683I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-22.63381632+81.96203679I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-22.63381646+81.96203679I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-22.63381644+81.96203672I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E31	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=W_{\kappa,-\mu}\left% (z\right)}}$	`WhittakerW(kappa, mu, z)= WhittakerW(kappa, - mu, z)`	`WhittakerW[\[Kappa], \[Mu], z]= WhittakerW[\[Kappa], - \[Mu], z]`	Successful	Successful	-	-
13.14.E32	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=\frac{e^{+(\kappa-\mu-\frac{1}{2})\pi\mathrm{i}}}{\Gamma\left(% \frac{1}{2}+\mu+\kappa\right)}W_{\kappa,\mu}\left(z\right)+\frac{e^{+\kappa\pi% \mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}W_{-\kappa,\mu}\left(e^% {+\pi\mathrm{i}}z\right)}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, z)=(exp(+(kappa - mu -(1)/(2))* PiI))/(GAMMA((1)/(2)+ mu + kappa))WhittakerW(kappa, mu, z)+(exp(+ kappaPiI))/(GAMMA((1)/(2)+ mu - kappa))WhittakerW(- kappa, mu, exp(+ PiI)*z)`	`Divide[1,Gamma[1 + 2\[Mu]]]WhittakerM[\[Kappa], \[Mu], z]=Divide[Exp[+(\[Kappa]- \[Mu]-Divide[1,2])* PiI],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]WhittakerW[\[Kappa], \[Mu], z]+Divide[Exp[+ \[Kappa]PiI],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]WhittakerW[- \[Kappa], \[Mu], Exp[+ PiI]*z]`	Failure	Failure	Fail `1.298497732-.1938713855e-1I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `1.187122752-1.346515592I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-9.654177833-4.981936798I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `34.26140886+126.3803650I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E32	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=\frac{e^{-(\kappa-\mu-\frac{1}{2})\pi\mathrm{i}}}{\Gamma\left(% \frac{1}{2}+\mu+\kappa\right)}W_{\kappa,\mu}\left(z\right)+\frac{e^{-\kappa\pi% \mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}W_{-\kappa,\mu}\left(e^% {-\pi\mathrm{i}}z\right)}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, z)=(exp(-(kappa - mu -(1)/(2))* PiI))/(GAMMA((1)/(2)+ mu + kappa))WhittakerW(kappa, mu, z)+(exp(- kappaPiI))/(GAMMA((1)/(2)+ mu - kappa))WhittakerW(- kappa, mu, exp(- PiI)*z)`	`Divide[1,Gamma[1 + 2\[Mu]]]WhittakerM[\[Kappa], \[Mu], z]=Divide[Exp[-(\[Kappa]- \[Mu]-Divide[1,2])* PiI],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]WhittakerW[\[Kappa], \[Mu], z]+Divide[Exp[- \[Kappa]PiI],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]WhittakerW[- \[Kappa], \[Mu], Exp[- PiI]*z]`	Failure	Failure	Fail `579.6433793+324.2736386I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `201.3880428-41.30381202I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-8591.170394-81467.17807I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `-198894.9185-2104750.118I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` ... skip entries to safe data	Skip
13.14.E33	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(-2% \mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}M_{\kappa,\mu}\left(z% \right)+\frac{\Gamma\left(2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa% \right)}M_{\kappa,-\mu}\left(z\right)}}$	`WhittakerW(kappa, mu, z)=(GAMMA(- 2mu))/(GAMMA((1)/(2)- mu - kappa))WhittakerM(kappa, mu, z)+(GAMMA(2mu))/(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
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 -(1)/(2))* WhittakerM(kappa - 1, mu, z)+(z - 2kappa) 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	-	-
13.15.E2	${\displaystyle{\displaystyle 2\mu(1+2\mu)\sqrt{z}M_{\kappa-\frac{1}{2},\mu-% \frac{1}{2}}\left(z\right)-(z+2\mu)(1+2\mu)M_{\kappa,\mu}\left(z\right)+(% \kappa+\mu+\tfrac{1}{2})\sqrt{z}M_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z% \right)=0}}$	`2mu(1 + 2mu)sqrt(z)WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)-(z + 2mu)(1 + 2mu)* 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	-	Successful
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 -(1)/(2))* WhittakerM(kappa -(1)/(2), mu +(1)/(2), z)+(1 + 2mu)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	-	Successful
13.15.E4	${\displaystyle{\displaystyle 2\mu M_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(% z\right)-2\mu M_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-\sqrt{z}M_{% \kappa,\mu}\left(z\right)=0}}$	`2muWhittakerM(kappa -(1)/(2), mu -(1)/(2), z)- 2muWhittakerM(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	-	Successful
13.15.E5	${\displaystyle{\displaystyle 2\mu(1+2\mu)M_{\kappa,\mu}\left(z\right)-2\mu(1+2% \mu)\sqrt{z}M_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-(\kappa-\mu-% \tfrac{1}{2})\sqrt{z}M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$	`2mu(1 + 2mu) WhittakerM(kappa, mu, z)- 2mu(1 + 2mu)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	-	Successful
13.15.E6	${\displaystyle{\displaystyle 2\mu(1+2\mu)\sqrt{z}M_{\kappa+\frac{1}{2},\mu-% \frac{1}{2}}\left(z\right)+(z-2\mu)(1+2\mu)M_{\kappa,\mu}\left(z\right)+(% \kappa-\mu-\tfrac{1}{2})\sqrt{z}M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z% \right)=0}}$	`2mu(1 + 2mu)sqrt(z)WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)+(z - 2mu)(1 + 2mu)* 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	-	Successful
13.15.E7	${\displaystyle{\displaystyle 2\mu(1+2\mu)\sqrt{z}M_{\kappa+\frac{1}{2},\mu-% \frac{1}{2}}\left(z\right)-2\mu(1+2\mu)M_{\kappa,\mu}\left(z\right)+(\kappa+% \mu+\tfrac{1}{2})\sqrt{z}M_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=% 0}}$	`2mu(1 + 2mu)sqrt(z)WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)- 2mu(1 + 2mu)* 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	-	Successful
13.15.E8	${\displaystyle{\displaystyle W_{\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z% \right)-\sqrt{z}W_{\kappa,\mu}\left(z\right)+(\kappa-\mu-\tfrac{1}{2})W_{% \kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0}}$	`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	-	Skip
13.15.E9	${\displaystyle{\displaystyle W_{\kappa+\frac{1}{2},\mu-\frac{1}{2}}\left(z% \right)-\sqrt{z}W_{\kappa,\mu}\left(z\right)+(\kappa+\mu-\tfrac{1}{2})W_{% \kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)=0}}$	`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	-	Skip
13.15.E10	${\displaystyle{\displaystyle 2\mu W_{\kappa,\mu}\left(z\right)-\sqrt{z}W_{% \kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)+\sqrt{z}W_{\kappa+\frac{1}{2% },\mu-\frac{1}{2}}\left(z\right)=0}}$	`2muWhittakerW(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	-	Skip
13.15.E11	${\displaystyle{\displaystyle W_{\kappa+1,\mu}\left(z\right)+(2\kappa-z)W_{% \kappa,\mu}\left(z\right)+(\kappa-\mu-\tfrac{1}{2})(\kappa+\mu-\tfrac{1}{2})W_% {\kappa-1,\mu}\left(z\right)=0}}$	`WhittakerW(kappa + 1, mu, z)+(2kappa - 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	-	-
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 -(1)/(2))sqrt(z)WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)+ 2muWhittakerW(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	-	Skip
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 -(1)/(2))sqrt(z)WhittakerW(kappa -(1)/(2), mu -(1)/(2), z)-(z + 2mu) 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	-	Skip
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 -(1)/(2))sqrt(z)WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)-(z - 2mu) 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	-	Skip
13.15.E15	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {\frac{1}{2}z}z^{\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{% \left(-2\mu\right)_{n}}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}M_{\kappa-\frac% {1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$	`diff(exp((1)/(2)z)(z)^(mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(- 1)^(n)* pochhammer(- 2mu, 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	Skip	Skip
13.15.E16	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {\frac{1}{2}z}z^{-\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=\frac{{% \left(\frac{1}{2}+\mu-\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^{\frac{1% }{2}z}z^{-\mu-\frac{1}{2}(n+1)}M_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z% \right)}}$	`diff(exp((1)/(2)z)(z)^(- mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(pochhammer((1)/(2)+ mu - kappa, n))/(pochhammer(1 + 2mu, 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	Skip	Skip
13.15.E17	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(e^{\frac{1}{2}z}z^{-\kappa-1}M_{\kappa,\mu}\left(z\right)\right)={\left(% \tfrac{1}{2}+\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{n-\kappa-1}M_{\kappa-n,% \mu}\left(z\right)}}$	`(zdiff(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)`	`(zD[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	Fail `.422889411+.400864309e-1I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `.3423332190-2.928704994I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `28.78460329-27.79294397I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `.8091469094-.1815739427I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.15.E18	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-\frac{1}{2}z}z^{\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}% {\left(-2\mu\right)_{n}}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}M_{\kappa+% \frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$	`diff(exp(-(1)/(2)z)(z)^(mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(- 1)^(n)* pochhammer(- 2mu, 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	Skip	Skip
13.15.E19	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n% }\frac{{\left(\frac{1}{2}+\mu+\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^% {-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*M_{\kappa+\frac{1}{2}n,\mu+\frac{1}{% 2}n}\left(z\right)}}$	`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 + 2mu, 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	Skip	Skip
13.15.E20	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(e^{-\frac{1}{2}z}z^{\kappa-1}M_{\kappa,\mu}\left(z\right)\right)={\left(% \tfrac{1}{2}+\mu+\kappa\right)_{n}}e^{-\frac{1}{2}z}z^{\kappa+n-1}\*M_{\kappa+% n,\mu}\left(z\right)}}$	`(zdiff(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)`	`(zD[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	Fail `.3651560696+.5317892033I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-2.267246204+4.379959380I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `-31.10787298-.100038800I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `29.73991513-87.25229264I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.15.E21	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {\frac{1}{2}z}z^{-\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}% {\left(\tfrac{1}{2}+\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(% n+1)}\*W_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right)}}$	`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	Skip	Skip
13.15.E22	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {\frac{1}{2}z}z^{\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{% \left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+% 1)}\*W_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right)}}$	`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	Skip	Skip
13.15.E23	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(e^{\frac{1}{2}z}z^{-\kappa-1}W_{\kappa,\mu}\left(z\right)\right)={\left(% \tfrac{1}{2}+\mu-\kappa\right)_{n}}{\left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e% ^{\frac{1}{2}z}z^{n-\kappa-1}W_{\kappa-n,\mu}\left(z\right)}}$	`(zdiff(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)`	`(zD[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	Fail `2.287537999+5.448901962I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `12.33305908+8.582530455I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `22.68496902-17.41418341I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `.1675216432+.4056625244I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.15.E24	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n% }e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}W_{\kappa+\frac{1}{2}n,\mu+\frac{1}% {2}n}\left(z\right)}}$	`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	Skip	Skip
13.15.E25	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-\frac{1}{2}z}z^{\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}% e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}W_{\kappa+\frac{1}{2}n,\mu-\frac{1}{2% }n}\left(z\right)}}$	`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	Skip	Skip
13.15.E26	${\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(e^{-\frac{1}{2}z}z^{\kappa-1}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n% }e^{-\frac{1}{2}z}z^{\kappa+n-1}W_{\kappa+n,\mu}\left(z\right)}}$	`(zdiff(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)`	`(zD[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	Fail `-.2720350864+.1235096327I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `-1.238205578-.8204474278I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `6.403097481-9.930704107I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `44.88142838-1.79519457I <- {kappa = 2^(1/2)+I2^(1/2), mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.16.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+% 2\mu\right)z^{\mu+\frac{1}{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa% \right)\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*\int_{-1}^{1}e^{\frac{1}{2}% zt}(1+t)^{\mu-\frac{1}{2}-\kappa}(1-t)^{\mu-\frac{1}{2}+\kappa}\mathrm{d}t}}$	`WhittakerM(kappa, mu, z)=(GAMMA(1 + 2mu)(z)^(mu +(1)/(2))* (2)^(- 2mu))/(GAMMA((1)/(2)+ mu - kappa)GAMMA((1)/(2)+ mu + kappa))* int(exp((1)/(2)zt)(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]zt](1 + t)^(\[Mu]-Divide[1,2]- \[Kappa])(1 - t)^(\[Mu]-Divide[1,2]+ \[Kappa]), {t, - 1, 1}]`	Failure	Failure	Skip	Error
13.16.E2	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+% 2\mu\right)z^{\lambda}}{\Gamma\left(1+2\mu-2\lambda\right)\Gamma\left(2\lambda% \right)}\*\int_{0}^{1}M_{\kappa-\lambda,\mu-\lambda}\left(zt\right)e^{\frac{1}% {2}z(t-1)}t^{\mu-\lambda-\frac{1}{2}}{(1-t)^{2\lambda-1}}\mathrm{d}t}}$	`WhittakerM(kappa, mu, z)=(GAMMA(1 + 2mu)(z)^(lambda))/(GAMMA(1 + 2mu - 2lambda)GAMMA(2lambda))* int(WhittakerM(kappa - lambda, mu - lambda, zt)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], zt]Exp[Divide[1,2]z(t - 1)](t)^(\[Mu]- \[Lambda]-Divide[1,2])(1 - t)^(2*\[Lambda]- 1), {t, 0, 1}]`	Failure	Failure	Skip	Error
13.16.E3	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=\frac{\sqrt{z}e^{\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu+% \kappa\right)}\int_{0}^{\infty}e^{-t}t^{\kappa-\frac{1}{2}}J_{2\mu}\left(2% \sqrt{zt}\right)\mathrm{d}t}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, z)=(sqrt(z)exp((1)/(2)z))/(GAMMA((1)/(2)+ mu + kappa))int(exp(- t)(t)^(kappa -(1)/(2))* BesselJ(2mu, 2sqrt(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], 2Sqrt[z*t]], {t, 0, Infinity}]`	Successful	Failure	-	Error
13.16.E4	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=\frac{\sqrt{z}e^{-\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-% \kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}I_{2\mu}\left(2% \sqrt{zt}\right)\mathrm{d}t}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, z)=(sqrt(z)exp(-(1)/(2)z))/(GAMMA((1)/(2)+ mu - kappa))* int(exp(- t)(t)^(- kappa -(1)/(2)) BesselI(2mu, 2sqrt(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], 2Sqrt[z*t]], {t, 0, Infinity}]`	Failure	Failure	Skip	Successful
13.16.E5	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{z^{\mu+\frac{1% }{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{1}^{\infty}e% ^{-\frac{1}{2}zt}(t-1)^{\mu-\frac{1}{2}-\kappa}(t+1)^{\mu-\frac{1}{2}+\kappa}% \mathrm{d}t}}$	`WhittakerW(kappa, mu, z)=((z)^(mu +(1)/(2))* (2)^(- 2mu))/(GAMMA((1)/(2)+ mu - kappa)) int(exp(-(1)/(2)zt)(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]zt](t - 1)^(\[Mu]-Divide[1,2]- \[Kappa])(t + 1)^(\[Mu]-Divide[1,2]+ \[Kappa]), {t, 1, Infinity}]`	Failure	Failure	Skip	Error
13.16.E6	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2% }z}z^{\kappa+1}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}% {2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{W_{-\kappa,\mu}\left(t\right)e^% {-\frac{1}{2}t}t^{-\kappa-1}}{t+z}\mathrm{d}t}}$	`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}]`	Failure	Failure	Skip	Error
13.16.E7	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{(-1)^{n}e^{-% \frac{1}{2}z}z^{\frac{1}{2}-\mu-n}}{\Gamma\left(1+2\mu\right)\Gamma\left(\frac% {1}{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{M_{-\kappa,\mu}\left(t\right% )e^{-\frac{1}{2}t}t^{n+\mu-\frac{1}{2}}}{t+z}\mathrm{d}t}}$	`WhittakerW(kappa, mu, z)=((- 1)^(n)* exp(-(1)/(2)z)(z)^((1)/(2)- mu - n))/(GAMMA(1 + 2mu)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}]`	Failure	Failure	Skip	Error
13.16.E8	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{2\sqrt{z}e^{-% \frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2% }-\mu-\kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}K_{2\mu}% \left(2\sqrt{zt}\right)\mathrm{d}t}}$	`WhittakerW(kappa, mu, z)=(2sqrt(z)exp(-(1)/(2)z))/(GAMMA((1)/(2)+ mu - kappa)GAMMA((1)/(2)- mu - kappa))* int(exp(- t)(t)^(- kappa -(1)/(2)) BesselK(2mu, 2sqrt(z*t)), t = 0..infinity)`	`WhittakerW[\[Kappa], \[Mu], z]=Divide[2Sqrt[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], 2Sqrt[z*t]], {t, 0, Infinity}]`	Successful	Failure	-	Error
13.16.E9	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \kappa+c}\*\int_{0}^{\infty}e^{-zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left({% \tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}-\mu-\kappa\atop c};-t\right)\mathrm{d}t}}$	`WhittakerW(kappa, mu, z)= exp(-(1)/(2)z)(z)^(kappa + c)* int(exp(- zt)(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[- zt](t)^(c - 1)* HypergeometricPFQRegularized[{Divide[1,2]+ \[Mu]- \[Kappa],Divide[1,2]- \[Mu]- \[Kappa]}, {c}, - t], {t, 0, Infinity}]`	Failure	Failure	Skip	Error
13.16.E10	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(e^{+\pi\mathrm{i}}z\right)=\frac{e^{\frac{1}{2}z+(\frac{1}{2}+\mu)\pi% \mathrm{i}}}{2\pi\mathrm{i}\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{-% \mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(t-\kappa\right)\Gamma% \left(\frac{1}{2}+\mu-t\right)}{\Gamma\left(\frac{1}{2}+\mu+t\right)}z^{t}% \mathrm{d}t}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, exp(+ PiI)z)=(exp((1)/(2)z +((1)/(2)+ mu) PiI))/(2PiIGAMMA((1)/(2)+ mu - kappa))* int((GAMMA(t - kappa)GAMMA((1)/(2)+ mu - t))/(GAMMA((1)/(2)+ mu + t))(z)^(t), t = - Iinfinity..Iinfinity)`	`Divide[1,Gamma[1 + 2\[Mu]]]WhittakerM[\[Kappa], \[Mu], Exp[+ PiI]z]=Divide[Exp[Divide[1,2]z +(Divide[1,2]+ \[Mu]) PiI],2PiIGamma[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, - IInfinity, IInfinity}]`	Error	Failure	-	Error
13.16.E10	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(e^{-\pi\mathrm{i}}z\right)=\frac{e^{\frac{1}{2}z-(\frac{1}{2}+\mu)\pi% \mathrm{i}}}{2\pi\mathrm{i}\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{-% \mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(t-\kappa\right)\Gamma% \left(\frac{1}{2}+\mu-t\right)}{\Gamma\left(\frac{1}{2}+\mu+t\right)}z^{t}% \mathrm{d}t}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, exp(- PiI)z)=(exp((1)/(2)z -((1)/(2)+ mu) PiI))/(2PiIGAMMA((1)/(2)+ mu - kappa))* int((GAMMA(t - kappa)GAMMA((1)/(2)+ mu - t))/(GAMMA((1)/(2)+ mu + t))(z)^(t), t = - Iinfinity..Iinfinity)`	`Divide[1,Gamma[1 + 2\[Mu]]]WhittakerM[\[Kappa], \[Mu], Exp[- PiI]z]=Divide[Exp[Divide[1,2]z -(Divide[1,2]+ \[Mu]) PiI],2PiIGamma[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, - IInfinity, IInfinity}]`	Error	Failure	-	Error
13.16.E11	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2% }z}}{2\pi\mathrm{i}}\*\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma% \left(\frac{1}{2}+\mu+t\right)\Gamma\left(\frac{1}{2}-\mu+t\right)\Gamma\left(% -\kappa-t\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1% }{2}-\mu-\kappa\right)}z^{-t}\mathrm{d}t}}$	`WhittakerW(kappa, mu, z)=(exp(-(1)/(2)z))/(2PiI) 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 = - Iinfinity..Iinfinity)`	`WhittakerW[\[Kappa], \[Mu], z]=Divide[Exp[-Divide[1,2]z],2PiI] 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, - IInfinity, IInfinity}]`	Error	Failure	-	Error
13.16.E12	${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{\frac{1}{2}% z}}{2\pi\mathrm{i}}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma% \left(\frac{1}{2}+\mu+t\right)\Gamma\left(\frac{1}{2}-\mu+t\right)}{\Gamma% \left(1-\kappa+t\right)}z^{-t}\mathrm{d}t}}$	`WhittakerW(kappa, mu, z)=(exp((1)/(2)z))/(2PiI)int((GAMMA((1)/(2)+ mu + t)GAMMA((1)/(2)- mu + t))/(GAMMA(1 - kappa + t))(z)^(- t), t = - Iinfinity..Iinfinity)`	`WhittakerW[\[Kappa], \[Mu], z]=Divide[Exp[Divide[1,2]z],2PiI]Integrate[Divide[Gamma[Divide[1,2]+ \[Mu]+ t]Gamma[Divide[1,2]- \[Mu]+ t],Gamma[1 - \[Kappa]+ t]](z)^(- t), {t, - IInfinity, IInfinity}]`	Failure	Failure	Skip	Error
13.18.E1	${\displaystyle{\displaystyle M_{0,\frac{1}{2}}\left(2z\right)=2\sinh z}}$	`WhittakerM(0, (1)/(2), 2z)= 2sinh(z)`	`WhittakerM[0, Divide[1,2], 2z]= 2Sinh[z]`	Successful	Successful	-	-
13.18.E2	${\displaystyle{\displaystyle M_{\kappa,\kappa-\frac{1}{2}}\left(z\right)=W_{% \kappa,\kappa-\frac{1}{2}}\left(z\right)}}$	`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	-	-
13.18.E2	${\displaystyle{\displaystyle W_{\kappa,\kappa-\frac{1}{2}}\left(z\right)=W_{% \kappa,-\kappa+\frac{1}{2}}\left(z\right)}}$	`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	-
13.18.E2	${\displaystyle{\displaystyle W_{\kappa,-\kappa+\frac{1}{2}}\left(z\right)=e^{-% \frac{1}{2}z}z^{\kappa}}}$	`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	Skip	-
13.18.E3	${\displaystyle{\displaystyle M_{\kappa,-\kappa-\frac{1}{2}}\left(z\right)=e^{% \frac{1}{2}z}z^{-\kappa}}}$	`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	-	-
13.18.E4	${\displaystyle{\displaystyle M_{\mu-\frac{1}{2},\mu}\left(z\right)=2\mu e^{% \frac{1}{2}z}z^{\frac{1}{2}-\mu}\gamma\left(2\mu,z\right)}}$	`WhittakerM(mu -(1)/(2), mu, z)= 2muexp((1)/(2)z)(z)^((1)/(2)- mu)* GAMMA(2mu)-GAMMA(2mu, 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	Fail `4.200609167-1.330017252I <- {mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2)}` `1.614512827-1.289496767I <- {mu = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2)}` `2101.588542-3319.229912I <- {mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-3.931276422-11.62291844I <- {mu = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	-
13.18.E5	${\displaystyle{\displaystyle W_{\mu-\frac{1}{2},\mu}\left(z\right)=e^{\frac{1}% {2}z}z^{\frac{1}{2}-\mu}\Gamma\left(2\mu,z\right)}}$	`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	-	-
13.18.E6	${\displaystyle{\displaystyle M_{-\frac{1}{4},\frac{1}{4}}\left(z^{2}\right)=% \tfrac{1}{2}e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\operatorname{erf}\left(z\right)}}$	`WhittakerM(-(1)/(4), (1)/(4), (z)^(2))=(1)/(2)exp((1)/(2)(z)^(2))sqrt(Piz)*erf(z)`	`WhittakerM[-Divide[1,4], Divide[1,4], (z)^(2)]=Divide[1,2]Exp[Divide[1,2](z)^(2)]Sqrt[Piz]*Erf[z]`	Failure	Failure	Fail `.4198419251+1.807257668I <- {z = -2^(1/2)-I2^(1/2)}` `.4198419251-1.807257668I <- {z = -2^(1/2)+I2^(1/2)}`	Fail `Complex[0.4198419223374512, 1.8072576674879106] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[0.4198419223374512, -1.8072576674879106] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.18.E7	${\displaystyle{\displaystyle W_{-\frac{1}{4},+\frac{1}{4}}\left(z^{2}\right)=e% ^{\frac{1}{2}z^{2}}\sqrt{\pi z}\operatorname{erfc}\left(z\right)}}$	`WhittakerW(-(1)/(4), +(1)/(4), (z)^(2))= exp((1)/(2)(z)^(2))sqrt(Piz)erfc(z)`	`WhittakerW[-Divide[1,4], +Divide[1,4], (z)^(2)]= Exp[Divide[1,2](z)^(2)]Sqrt[Piz]Erfc[z]`	Failure	Failure	Fail `-4.382229868-3.743892002I <- {z = -2^(1/2)-I2^(1/2)}` `-4.382229868+3.743892002I <- {z = -2^(1/2)+I2^(1/2)}`	Fail `Complex[-4.38222986299419, -3.7438920038513093] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.38222986299419, 3.7438920038513093] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.18.E7	${\displaystyle{\displaystyle W_{-\frac{1}{4},-\frac{1}{4}}\left(z^{2}\right)=e% ^{\frac{1}{2}z^{2}}\sqrt{\pi z}\operatorname{erfc}\left(z\right)}}$	`WhittakerW(-(1)/(4), -(1)/(4), (z)^(2))= exp((1)/(2)(z)^(2))sqrt(Piz)erfc(z)`	`WhittakerW[-Divide[1,4], -Divide[1,4], (z)^(2)]= Exp[Divide[1,2](z)^(2)]Sqrt[Piz]Erfc[z]`	Failure	Failure	Fail `-4.382229868-3.743892002I <- {z = -2^(1/2)-I2^(1/2)}` `-4.382229868+3.743892002I <- {z = -2^(1/2)+I2^(1/2)}`	Fail `Complex[-4.382229862994191, -3.7438920038513093] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-4.382229862994191, 3.7438920038513093] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.18.E8	${\displaystyle{\displaystyle M_{0,\nu}\left(2z\right)=2^{2\nu+\frac{1}{2}}% \Gamma\left(1+\nu\right)\sqrt{z}I_{\nu}\left(z\right)}}$	`WhittakerM(0, nu, 2z)= (2)^(2nu +(1)/(2))* GAMMA(1 + nu)sqrt(z)BesselI(nu, z)`	`WhittakerM[0, \[Nu], 2z]= (2)^(2\[Nu]+Divide[1,2])* Gamma[1 + \[Nu]]Sqrt[z]BesselI[\[Nu], z]`	Successful	Successful	-	-
13.18.E9	${\displaystyle{\displaystyle W_{0,\nu}\left(2z\right)=\sqrt{\ifrac{2z}{\pi}}K_% {\nu}\left(z\right)}}$	`WhittakerW(0, nu, 2z)=sqrt((2z)/(Pi))*BesselK(nu, z)`	`WhittakerW[0, \[Nu], 2z]=Sqrt[Divide[2z,Pi]]*BesselK[\[Nu], z]`	Successful	Successful	-	-
13.18.E10	${\displaystyle{\displaystyle W_{0,\frac{1}{3}}\left(\tfrac{4}{3}z^{\frac{3}{2}% }\right)=2\sqrt{\pi}z^{\frac{1}{4}}\mathrm{Ai}\left(z\right)}}$	`WhittakerW(0, (1)/(3), (4)/(3)(z)^((3)/(2)))= 2sqrt(Pi)(z)^((1)/(4)) AiryAi(z)`	`WhittakerW[0, Divide[1,3], Divide[4,3](z)^(Divide[3,2])]= 2Sqrt[Pi](z)^(Divide[1,4]) AiryAi[z]`	Failure	Failure	Fail `-.111157710+.128876647I <- {z = -2^(1/2)-I2^(1/2)}` `-.111157710-.128876647I <- {z = -2^(1/2)+I2^(1/2)}`	Fail `Complex[-0.11115770699234684, 0.12887664550372602] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.11115770699234684, -0.12887664550372602] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}`
13.18.E11	${\displaystyle{\displaystyle W_{-\frac{1}{2}a,+\frac{1}{4}}\left(\tfrac{1}{2}z% ^{2}\right)=2^{\frac{1}{2}a}\sqrt{z}U(a,z)}}$	`WhittakerW(-(1)/(2)a, +(1)/(4), (1)/(2)(z)^(2))= (2)^((1)/(2)a)sqrt(z)*CylinderU(a , z, $1)`	`WhittakerW[-Divide[1,2]a, +Divide[1,4], Divide[1,2](z)^(2)]= (2)^(Divide[1,2]a)Sqrt[z]*ParabolicCylinderD[-a , z - 1/2, $1]`	Error	Error	-	-
13.18.E11	${\displaystyle{\displaystyle W_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z% ^{2}\right)=2^{\frac{1}{2}a}\sqrt{z}U(a,z)}}$	`WhittakerW(-(1)/(2)a, -(1)/(4), (1)/(2)(z)^(2))= (2)^((1)/(2)a)sqrt(z)*CylinderU(a , z, $1)`	`WhittakerW[-Divide[1,2]a, -Divide[1,4], Divide[1,2](z)^(2)]= (2)^(Divide[1,2]a)Sqrt[z]*ParabolicCylinderD[-a , z - 1/2, $1]`	Error	Error	-	-
13.18.E12	${\displaystyle{\displaystyle M_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z% ^{2}\right)=2^{\frac{1}{2}a-1}\Gamma\left(\tfrac{1}{2}a+\tfrac{3}{4}\right)% \sqrt{\ifrac{z}{\pi}}\*\left(U\left(a,z\right)+U\left(a,-z\right)\right)}}$	`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[-a - 1/2, z]+ ParabolicCylinderD[-a - 1/2, - z])`	Failure	Failure	Fail `-1.595813139-1.786229512I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-6.548449077-7.324160790I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `-6.548449077+7.324160790I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-1.595813139+1.786229512I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[-1.5958131384127743, -1.7862295136979531] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-6.548449089259156, -7.324160795019219] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-6.548449089259156, 7.324160795019219] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-1.5958131384127743, 1.7862295136979531] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.18.E13	${\displaystyle{\displaystyle M_{-\frac{1}{2}a,\frac{1}{4}}\left(\tfrac{1}{2}z^% {2}\right)=2^{\frac{1}{2}a-2}\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{4}\right)% \sqrt{\ifrac{z}{\pi}}\*\left(U\left(a,-z\right)-U\left(a,z\right)\right)}}$	`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[-a - 1/2, - z]- ParabolicCylinderD[-a - 1/2, z])`	Failure	Failure	Fail `-.2924843841+.9350194047I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `2.175978499-4.464282068I <- {a = 2^(1/2)+I2^(1/2), z = -2^(1/2)+I2^(1/2)}` `2.175978499+4.464282068I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)-I2^(1/2)}` `-.2924843841-.9350194047I <- {a = 2^(1/2)-I2^(1/2), z = -2^(1/2)+I2^(1/2)}` ... skip entries to safe data	Fail `Complex[-0.29248438571599344, 0.9350194045102764] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[2.175978498735585, -4.464282074060343] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` `Complex[2.175978498735585, 4.464282074060343] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.29248438571599344, -0.9350194045102764] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.18.E14	${\displaystyle{\displaystyle M_{\frac{1}{4}+n,-\frac{1}{4}}\left(z^{2}\right)=% (-1)^{n}\frac{n!}{(2n)!}e^{-\frac{1}{2}z^{2}}\sqrt{z}H_{2n}\left(z\right)}}$	`WhittakerM((1)/(4)+ n, -(1)/(4), (z)^(2))=(- 1)^(n)(factorial(n))/(factorial(2n))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)!,(2n)!]Exp[-Divide[1,2](z)^(2)]Sqrt[z]HermiteH[2*n, z]`	Failure	Failure	Fail `-10.35742410-12.35814572I <- {z = -2^(1/2)-I2^(1/2), n = 1}` `-51.12520045+7.99947819I <- {z = -2^(1/2)-I2^(1/2), n = 2}` `-70.94025645+106.0858980I <- {z = -2^(1/2)-I2^(1/2), n = 3}` `-10.35742410+12.35814572I <- {z = -2^(1/2)+I2^(1/2), n = 1}` ... skip entries to safe data	Fail `Complex[-10.357424118634546, -12.358145719594317] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-51.125200492418, 7.999478257226418] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-70.9402563798825, 106.08589822655182] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-10.357424118634546, 12.358145719594317] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.18.E15	${\displaystyle{\displaystyle M_{\frac{3}{4}+n,\frac{1}{4}}\left(z^{2}\right)=(% -1)^{n}\frac{n!}{(2n+1)!}\frac{e^{-\frac{1}{2}z^{2}}\sqrt{z}}{2}H_{2n+1}\left(% z\right)}}$	`WhittakerM((3)/(4)+ n, (1)/(4), (z)^(2))=(- 1)^(n)(factorial(n))/(factorial(2n + 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)!,(2n + 1)!]Divide[Exp[-Divide[1,2](z)^(2)]Sqrt[z],2]HermiteH[2*n + 1, z]`	Failure	Failure	Fail `-10.80554626-3.608039299I <- {z = -2^(1/2)-I2^(1/2), n = 1}` `-20.84223327+13.83655303I <- {z = -2^(1/2)-I2^(1/2), n = 2}` `-10.76427954+47.62458665I <- {z = -2^(1/2)-I2^(1/2), n = 3}` `-10.80554626+3.608039299I <- {z = -2^(1/2)+I2^(1/2), n = 1}` ... skip entries to safe data	Fail `Complex[-10.805546272663701, -3.6080392912358032] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-20.84223327255954, 13.836553078751255] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-10.764279468212877, 47.6245867445262] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-10.805546272663701, 3.6080392912358032] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.18.E16	${\displaystyle{\displaystyle W_{\frac{1}{4}+\frac{1}{2}n,\frac{1}{4}}\left(z^{% 2}\right)=2^{-n}e^{-\frac{1}{2}z^{2}}\sqrt{z}H_{n}\left(z\right)}}$	`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	Fail `-.145985934-3.997335125I <- {z = -2^(1/2)-I2^(1/2), n = 1}` `5.178712051+6.179072864I <- {z = -2^(1/2)-I2^(1/2), n = 2}` `16.20831939+5.412058949I <- {z = -2^(1/2)-I2^(1/2), n = 3}` `-.145985934+3.997335125I <- {z = -2^(1/2)+I2^(1/2), n = 1}` ... skip entries to safe data	Fail `Complex[-0.1459859378673154, -3.997335125548645] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[5.178712059317274, 6.179072859797158] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[16.208319408995553, 5.412058936853704] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}` `Complex[-0.1459859378673154, 3.997335125548645] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.18.E17	${\displaystyle{\displaystyle W_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}% \alpha}\left(z\right)=(-1)^{n}{\left(\alpha+1\right)_{n}}M_{\frac{1}{2}\alpha+% \frac{1}{2}+n,\frac{1}{2}\alpha}\left(z\right)}}$	`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	Successful
13.20.E9	${\displaystyle{\displaystyle\zeta\sqrt{\zeta^{2}+\alpha^{2}}+\alpha^{2}% \operatorname{arcsinh}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}-\frac{2% \kappa}{\mu}\ln\left(\frac{X+x-2\kappa}{2\sqrt{\mu^{2}-\kappa^{2}}}\right)-2% \ln\left(\frac{\mu X+2\mu^{2}-\kappa x}{x\sqrt{\mu^{2}-\kappa^{2}}}\right)}}$	`zetasqrt((zeta)^(2)+ (alpha)^(2))+ (alpha)^(2) arcsinh((zeta)/(alpha))=(X)/(mu)-(2kappa)/(mu)ln((X + x - 2kappa)/(2sqrt((mu)^(2)- (kappa)^(2))))- 2ln((muX + 2(mu)^(2)- kappax)/(x*sqrt((mu)^(2)- (kappa)^(2))))`	`\[zeta]Sqrt[(\[zeta])^(2)+ (\[Alpha])^(2)]+ (\[Alpha])^(2) ArcSinh[Divide[\[zeta],\[Alpha]]]=Divide[X,\[Mu]]-Divide[2\[Kappa],\[Mu]]Log[Divide[X + x - 2\[Kappa],2Sqrt[(\[Mu])^(2)- (\[Kappa])^(2)]]]- 2Log[Divide[\[Mu]X + 2(\[Mu])^(2)- \[Kappa]x,x*Sqrt[(\[Mu])^(2)- (\[Kappa])^(2)]]]`	Failure	Failure	Skip	Error
13.20.E10	${\displaystyle{\displaystyle\zeta=+\sqrt{\frac{x}{\mu}-2-2\ln\left(\frac{x}{2% \mu}\right)}}}$	`zeta = +sqrt((x)/(mu)- 2 - 2ln((x)/(2mu)))`	`\[zeta]= +Sqrt[Divide[x,\[Mu]]- 2 - 2Log[Divide[x,2\[Mu]]]]`	Failure	Failure	Fail `.234294656+.8983972080I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)+I2^(1/2), x = 1}` `.7206264000+.7915884667I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)+I2^(1/2), x = 2}` `1.051794028+.7104212616I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)+I2^(1/2), x = 3}` `.234294656-1.930029916I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)-I2^(1/2), x = 1}` ... skip entries to safe data	Error
13.20.E10	${\displaystyle{\displaystyle\zeta=-\sqrt{\frac{x}{\mu}-2-2\ln\left(\frac{x}{2% \mu}\right)}}}$	`zeta = -sqrt((x)/(mu)- 2 - 2ln((x)/(2mu)))`	`\[zeta]= -Sqrt[Divide[x,\[Mu]]- 2 - 2Log[Divide[x,2\[Mu]]]]`	Failure	Failure	Fail `2.594132468+1.930029916I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)+I2^(1/2), x = 1}` `2.107800724+2.036838657I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)+I2^(1/2), x = 2}` `1.776633096+2.118005862I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)+I2^(1/2), x = 3}` `2.594132468-.8983972080I <- {mu = 2^(1/2)+I2^(1/2), zeta = 2^(1/2)-I2^(1/2), x = 1}` ... skip entries to safe data	Error
13.20.E13	${\displaystyle{\displaystyle\zeta\sqrt{\zeta^{2}-\alpha^{2}}-\alpha^{2}% \operatorname{arccosh}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}-\frac{2% \kappa}{\mu}\ln\left(\frac{X+x-2\kappa}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)-2% \ln\left(\frac{\kappa x-\mu X-2\mu^{2}}{x\sqrt{\kappa^{2}-\mu^{2}}}\right)}}$	`zetasqrt((zeta)^(2)- (alpha)^(2))- (alpha)^(2) arccosh((zeta)/(alpha))=(X)/(mu)-(2kappa)/(mu)ln((X + x - 2kappa)/(2sqrt((kappa)^(2)- (mu)^(2))))- 2ln((kappax - muX - 2(mu)^(2))/(x*sqrt((kappa)^(2)- (mu)^(2))))`	`\[zeta]Sqrt[(\[zeta])^(2)- (\[Alpha])^(2)]- (\[Alpha])^(2) ArcCosh[Divide[\[zeta],\[Alpha]]]=Divide[X,\[Mu]]-Divide[2\[Kappa],\[Mu]]Log[Divide[X + x - 2\[Kappa],2Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]- 2Log[Divide[\[Kappa]x - \[Mu]X - 2(\[Mu])^(2),x*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]`	Error	Failure	-	Error
13.20.E14	${\displaystyle{\displaystyle\zeta\sqrt{\alpha^{2}-\zeta^{2}}+\alpha^{2}% \operatorname{arcsin}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}+\frac{2% \kappa}{\mu}\operatorname{arctan}\left(\frac{x-2\kappa}{X}\right)-2% \operatorname{arctan}\left(\frac{\kappa x-2\mu^{2}}{\mu X}\right)}}$	`zetasqrt((alpha)^(2)- (zeta)^(2))+ (alpha)^(2) arcsin((zeta)/(alpha))=(X)/(mu)+(2kappa)/(mu)arctan((x - 2kappa)/(X))- 2arctan((kappax - 2(mu)^(2))/(mu*X))`	`\[zeta]Sqrt[(\[Alpha])^(2)- (\[zeta])^(2)]+ (\[Alpha])^(2) ArcSin[Divide[\[zeta],\[Alpha]]]=Divide[X,\[Mu]]+Divide[2\[Kappa],\[Mu]]ArcTan[Divide[x - 2\[Kappa],X]]- 2ArcTan[Divide[\[Kappa]x - 2(\[Mu])^(2),\[Mu]*X]]`	Error	Failure	-	Error
13.20.E15	${\displaystyle{\displaystyle-\zeta\sqrt{\zeta^{2}-\alpha^{2}}-\alpha^{2}% \operatorname{arccosh}\left(-\frac{\zeta}{\alpha}\right)=-\frac{X}{\mu}+\frac{% 2\kappa}{\mu}\ln\left(\frac{2\kappa-X-x}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)+2% \ln\left(\frac{\mu X+2\mu^{2}-\kappa x}{x\sqrt{\kappa^{2}-\mu^{2}}}\right)}}$	`- zetasqrt((zeta)^(2)- (alpha)^(2))- (alpha)^(2) arccosh(-(zeta)/(alpha))= -(X)/(mu)+(2kappa)/(mu)ln((2kappa - X - x)/(2sqrt((kappa)^(2)- (mu)^(2))))+ 2ln((muX + 2(mu)^(2)- kappax)/(x*sqrt((kappa)^(2)- (mu)^(2))))`	`- \[zeta]Sqrt[(\[zeta])^(2)- (\[Alpha])^(2)]- (\[Alpha])^(2) ArcCosh[-Divide[\[zeta],\[Alpha]]]= -Divide[X,\[Mu]]+Divide[2\[Kappa],\[Mu]]Log[Divide[2\[Kappa]- X - x,2Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]+ 2Log[Divide[\[Mu]X + 2(\[Mu])^(2)- \[Kappa]x,x*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]`	Error	Failure	-	Error
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)]+ Log[Sqrt[x]+Sqrt[1 + x]]`	Failure	Failure	Fail `.3175387811+1.082392200I <- {zeta = 2^(1/2)+I2^(1/2), x = 1}` `-.982579648+1.082392200I <- {zeta = 2^(1/2)+I2^(1/2), x = 2}` `-2.167933582+1.082392200I <- {zeta = 2^(1/2)+I2^(1/2), x = 3}` `.3175387811-1.082392200I <- {zeta = 2^(1/2)-I2^(1/2), x = 1}` ... skip entries to safe data	Error
13.21.E11	${\displaystyle{\displaystyle\sqrt{4\mu^{2}-\kappa\zeta}-\mu\ln\left(\frac{2\mu% +\sqrt{4\mu^{2}-\kappa\zeta}}{2\mu-\sqrt{4\mu^{2}-\kappa\zeta}}\right)=\tfrac{% 1}{2}X+\mu\ln\left(\frac{x\sqrt{\kappa^{2}-\mu^{2}}}{2\mu^{2}-\kappa x+\mu X}% \right)+\kappa\ln\left(\frac{2\sqrt{\kappa^{2}-\mu^{2}}}{2\kappa-x-X}\right)}}$	`sqrt(4(mu)^(2)- kappazeta)- muln((2mu +sqrt(4(mu)^(2)- kappazeta))/(2mu -sqrt(4(mu)^(2)- kappazeta)))=(1)/(2)X + muln((xsqrt((kappa)^(2)- (mu)^(2)))/(2(mu)^(2)- kappax + muX))+ kappaln((2sqrt((kappa)^(2)- (mu)^(2)))/(2kappa - x - X))`	`Sqrt[4(\[Mu])^(2)- \[Kappa]\[zeta]]- \[Mu]Log[Divide[2\[Mu]+Sqrt[4(\[Mu])^(2)- \[Kappa]\[zeta]],2\[Mu]-Sqrt[4(\[Mu])^(2)- \[Kappa]\[zeta]]]]=Divide[1,2]X + \[Mu]Log[Divide[xSqrt[(\[Kappa])^(2)- (\[Mu])^(2)],2(\[Mu])^(2)- \[Kappa]x + \[Mu]X]]+ \[Kappa]Log[Divide[2Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)],2\[Kappa]- x - X]]`	Error	Failure	-	Error
13.21.E12	${\displaystyle{\displaystyle\sqrt{\kappa\zeta-4\mu^{2}}-2\mu\operatorname{% arctan}\left(\frac{\sqrt{\kappa\zeta-4\mu^{2}}}{2\mu}\right)=\tfrac{1}{2}(X-% \pi\mu)-\mu\operatorname{arctan}\left(\frac{x\kappa-2\mu^{2}}{\mu X}\right)+% \kappa\operatorname{arcsin}\left(\frac{X}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)}}$	`sqrt(kappazeta - 4(mu)^(2))- 2muarctan((sqrt(kappazeta - 4(mu)^(2)))/(2mu))=(1)/(2)(X - Pimu)- muarctan((xkappa - 2(mu)^(2))/(muX))+ kappaarcsin((X)/(2*sqrt((kappa)^(2)- (mu)^(2))))`	`Sqrt[\[Kappa]\[zeta]- 4(\[Mu])^(2)]- 2\[Mu]ArcTan[Divide[Sqrt[\[Kappa]\[zeta]- 4(\[Mu])^(2)],2\[Mu]]]=Divide[1,2](X - Pi\[Mu])- \[Mu]ArcTan[Divide[x\[Kappa]- 2(\[Mu])^(2),\[Mu]X]]+ \[Kappa]ArcSin[Divide[X,2*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]`	Error	Failure	-	Error
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(exp(- zt)(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[- zt](t)^(\[Nu]- 1)* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}]=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	Failure	Skip	Error
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(exp(- zt)(t)^(mu -(1)/(2))* WhittakerM(kappa, mu, t), t = 0..infinity)= GAMMA(2mu + 1)(z +(1)/(2))^(- kappa - mu -(1)/(2))*(z -(1)/(2))^(kappa - mu -(1)/(2))`	`Integrate[Exp[- zt](t)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}]= Gamma[2\[Mu]+ 1](z +Divide[1,2])^(- \[Kappa]- \[Mu]-Divide[1,2])*(z -Divide[1,2])^(\[Kappa]- \[Mu]-Divide[1,2])`	Failure	Failure	Skip	Error
13.23.E3	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{% \infty}e^{-\frac{1}{2}t}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac% {\Gamma\left(\mu+\nu+\frac{1}{2}\right)\Gamma\left(\kappa-\nu\right)}{\Gamma% \left(\frac{1}{2}+\mu+\kappa\right)\Gamma\left(\frac{1}{2}+\mu-\nu\right)}}}$	`(1)/(GAMMA(1 + 2mu))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}]=Divide[Gamma[\[Mu]+ \[Nu]+Divide[1,2]]Gamma[\[Kappa]- \[Nu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]Gamma[Divide[1,2]+ \[Mu]- \[Nu]]]`	Failure	Failure	Skip	Error
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(exp(- zt)(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[- zt](t)^(\[Nu]- 1)* WhittakerW[\[Kappa], \[Mu], t], {t, 0, Infinity}]= 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	Failure	Skip	Error
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(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}]=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	Failure	Skip	Error
13.23.E6	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)2\pi\mathrm{i}}% \int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}M_{\kappa,\mu}\left(t^{% -1}\right)\mathrm{d}t=\frac{z^{-\kappa-\frac{1}{2}}}{\Gamma\left(\frac{1}{2}+% \mu-\kappa\right)}I_{2\mu}\left(2\sqrt{z}\right)}}$	`(1)/(GAMMA(1 + 2mu)2PiI)int(exp(zt +(1)/(2)(t)^(- 1))(t)^(kappa)* WhittakerM(kappa, mu, (t)^(- 1)), t = - infinity..(0 +))=((z)^(- kappa -(1)/(2)))/(GAMMA((1)/(2)+ mu - kappa))BesselI(2mu, 2*sqrt(z))`	`Divide[1,Gamma[1 + 2\[Mu]]2PiI]Integrate[Exp[zt +Divide[1,2](t)^(- 1)](t)^(\[Kappa])* WhittakerM[\[Kappa], \[Mu], (t)^(- 1)], {t, - Infinity, (0 +)}]=Divide[(z)^(- \[Kappa]-Divide[1,2]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]BesselI[2\[Mu], 2*Sqrt[z]]`	Error	Failure	-	Error
13.23.E7	${\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e^{zt% +\frac{1}{2}t^{-1}}t^{\kappa}W_{\kappa,\mu}\left(t^{-1}\right)\mathrm{d}t=% \frac{2z^{-\kappa-\frac{1}{2}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)% \Gamma\left(\frac{1}{2}-\mu-\kappa\right)}K_{2\mu}\left(2\sqrt{z}\right)}}$	`(1)/(2PiI)int(exp(zt +(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(2mu, 2*sqrt(z))`	`Divide[1,2PiI]Integrate[Exp[zt +Divide[1,2](t)^(- 1)](t)^(\[Kappa])* WhittakerW[\[Kappa], \[Mu], (t)^(- 1)], {t, - Infinity, (0 +)}]=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	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{% \infty}\cos\left(2xt\right)e^{-\frac{1}{2}t^{2}}t^{-2\mu-1}M_{\kappa,\mu}\left% (t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}e^{-\frac{1}{2}x^{2}}x^{\mu+\kappa-1}% }{2\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}W_{\frac{1}{2}\kappa-\frac{3}{2}% \mu,\frac{1}{2}\kappa+\frac{1}{2}\mu}\left(x^{2}\right)}}$	`(1)/(GAMMA(1 + 2mu))int(cos(2xt)exp(-(1)/(2)(t)^(2))(t)^(- 2mu - 1)* WhittakerM(kappa, mu, (t)^(2)), t = 0..infinity)=(sqrt(Pi)exp(-(1)/(2)(x)^(2))(x)^(mu + kappa - 1))/(2GAMMA((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[2xt]Exp[-Divide[1,2](t)^(2)](t)^(- 2\[Mu]- 1)* WhittakerM[\[Kappa], \[Mu], (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi]Exp[-Divide[1,2](x)^(2)](x)^(\[Mu]+ \[Kappa]- 1),2Gamma[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	Failure	Skip	Error
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(exp(-(1)/(2)t)(t)^(mu -(1)/(2)(nu + 1)) WhittakerM(kappa, mu, t)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)=(GAMMA(1 + 2mu))/(GAMMA((1)/(2)- mu + kappa + nu))* exp(-(1)/(2)x)(x)^((1)/(2)(kappa - mu -(3)/(2))) WhittakerM((1)/(2)(kappa + 3mu - 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], 2Sqrt[xt]], {t, 0, Infinity}]=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	Failure	Skip	Error
13.23.E10	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{% \infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}M_{\kappa,\mu}\left(t\right)% J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{e^{-\frac{1}{2}x}x^{\frac{1}{2% }(\kappa+\mu-\frac{3}{2})}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*W_{% \frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2}),\frac{1}{2}(\kappa+\mu-\nu-\frac{1}{2% })}\left(x\right)}}$	`(1)/(GAMMA(1 + 2mu))int(exp(-(1)/(2)t)(t)^((1)/(2)(nu - 1)- mu) WhittakerM(kappa, mu, t)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)=(exp(-(1)/(2)x)(x)^((1)/(2)(kappa + mu -(3)/(2))))/(GAMMA((1)/(2)+ mu + kappa))* WhittakerW((1)/(2)(kappa - 3mu + 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], 2Sqrt[xt]], {t, 0, Infinity}]=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	Failure	Skip	Error
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(exp((1)/(2)t)(t)^((1)/(2)(nu - 1)- mu) WhittakerW(kappa, mu, t)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)=(GAMMA(nu - 2mu + 1))/(GAMMA((1)/(2)+ mu - kappa))* exp((1)/(2)x)(x)^((1)/(2)(mu - kappa -(3)/(2))) WhittakerW((1)/(2)(kappa + 3mu - 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], 2Sqrt[xt]], {t, 0, Infinity}]=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	Failure	Skip	Error
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(exp(-(1)/(2)t)(t)^((1)/(2)(nu - 1)- mu) WhittakerW(kappa, mu, t)BesselJ(nu, 2sqrt(xt)), t = 0..infinity)=(GAMMA(nu - 2mu + 1))/(GAMMA((3)/(2)- mu - kappa + nu))* exp(-(1)/(2)x)(x)^((1)/(2)(mu + kappa -(3)/(2))) WhittakerM((1)/(2)(kappa - 3mu + 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], 2Sqrt[xt]], {t, 0, Infinity}]=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	Failure	Skip	Error
13.24.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\Gamma\left(\kappa+% \mu\right)2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\\sum_{s=0}^{\infty}(-1)^{s}% \frac{{\left(2\kappa+2\mu\right)_{s}}{\left(2\kappa\right)_{s}}}{{\left(1+2\mu% \right)_{s}}s!}\\left(\kappa+\mu+s\right)I_{\kappa+\mu+s}\left(\tfrac{1}{2}z% \right)}}$	`WhittakerM(kappa, mu, z)= GAMMA(kappa + mu)(2)^(2kappa + 2mu) (z)^((1)/(2)- kappa)* sum((- 1)^(s)(pochhammer(2kappa + 2mu, s)pochhammer(2kappa, s))/(pochhammer(1 + 2mu, 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}]`	Failure	Failure	Skip	Skip
13.24.E2	${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=2^{2\mu}z^{\mu+\frac{1}{2}}\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)% \left(2\sqrt{\kappa z}\right)^{-2\mu-s}J_{2\mu+s}\left(2\sqrt{\kappa z}\right)}}$	`(1)/(GAMMA(1 + 2mu))WhittakerM(kappa, mu, z)= (2)^(2mu) sum(p(p[s])^(mu)(z)(2sqrt(kappaz))^(- 2mu - s) BesselJ(2mu + s, 2sqrt(kappa*z)), s = 0..infinity)`	`Divide[1,Gamma[1 + 2\[Mu]]]WhittakerM[\[Kappa], \[Mu], z]= (2)^(2\[Mu]) Sum[p(Subscript[p, s])^(\[Mu])(z)(2Sqrt[\[Kappa]z])^(- 2\[Mu]- s) BesselJ[2\[Mu]+ s, 2Sqrt[\[Kappa]*z]], {s, 0, Infinity}]`	Failure	Failure	Skip	Skip
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(-(1)/(2)z(coth(t)-(1)/(t)))((t)/(sinh(t)))^(1 - 2mu)sum(p(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[p(Subscript[p, s])^(\[Mu])(z)(-Divide[t,z])^(s), {s, 0, Infinity}]`	Failure	Failure	Skip	Skip
13.25.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)M_{\kappa,-\mu-1}% \left(z\right)+\frac{(\frac{1}{2}+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+% \mu)(1+2\mu)^{2}}M_{\kappa,\mu+1}\left(z\right)M_{\kappa,-\mu}\left(z\right)=1}}$	`WhittakerM(kappa, mu, z)WhittakerM(kappa, - mu - 1, z)+(((1)/(2)+ mu + kappa)((1)/(2)+ mu - kappa))/(4mu(1 + mu)(1 + 2mu)^(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	Successful	Successful
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)^(-(1)/(2)) (V[kappa ,(1)/(2)p])^(1)(2Ik*xi)`	`Subscript[f, 1](\[Xi])= (\[Xi])^(-Divide[1,2]) (Subscript[V, \[Kappa],Divide[1,2]p])^(1)(2Ik*\[Xi])`	Failure	Failure	Fail `5.226251858+1.835215598I <- {xi = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[1] = 2^(1/2)+I2^(1/2), k = 1}` `10.45250372-.329568802I <- {xi = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[1] = 2^(1/2)+I2^(1/2), k = 2}` `15.67875557-2.494353202I <- {xi = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[1] = 2^(1/2)+I2^(1/2), k = 3}` `9.226251856-2.164784400I <- {xi = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[1] = 2^(1/2)-I2^(1/2), k = 1}` ... skip entries to safe data	Fail `Complex[5.226251859505505, 1.8352155994152124] <- {Rule[k, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.45250371901101, -0.3295688011695752] <- {Rule[k, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[15.678755578516517, -2.4943532017543637] <- {Rule[k, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-2.164784400584788, -1.2262518595055054] <- {Rule[k, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` ... 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)^(-(1)/(2)) (V[kappa ,(1)/(2)p])^(2)(- 2Ik*eta)`	`Subscript[f, 2](\[Eta])= (\[Eta])^(-Divide[1,2]) (Subscript[V, \[Kappa],Divide[1,2]p])^(2)(- 2Ik*\[Eta])`	Failure	Failure	Fail `-10.45250371-.329568800I <- {eta = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[2] = 2^(1/2)+I2^(1/2), k = 1}` `-20.90500742-4.659137598I <- {eta = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[2] = 2^(1/2)+I2^(1/2), k = 2}` `-31.35751114-8.988706392I <- {eta = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[2] = 2^(1/2)+I2^(1/2), k = 3}` `-6.452503712-4.329568798I <- {eta = 2^(1/2)+I2^(1/2), V[kappa,1/2p] = 2^(1/2)+I2^(1/2), f[2] = 2^(1/2)-I2^(1/2), k = 1}` ... skip entries to safe data	Fail `Complex[-10.45250371901101, -0.3295688011695752] <- {Rule[k, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-20.90500743802202, -4.65913760233915] <- {Rule[k, 2], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[-31.35751115703303, -8.988706403508727] <- {Rule[k, 3], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}` `Complex[10.45250371901101, 8.329568801169575] <- {Rule[k, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}` ... skip entries to safe data
13.29.E3	${\displaystyle{\displaystyle e^{-\frac{1}{2}z}=\sum_{s=0}^{\infty}\frac{{\left% (2\mu\right)_{s}}{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(2\mu\right)% _{2s}}s!}(-z)^{s}y(s)}}$	`exp(-(1)/(2)z)= sum((pochhammer(2mu, s)pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(2mu, 2s)factorial(s))(- z)^(s) y*(s), s = 0..infinity)`	`Exp[-Divide[1,2]z]= Sum[Divide[Pochhammer[2\[Mu], s]Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[2\[Mu], 2s](s)!](- z)^(s) y*(s), {s, 0, Infinity}]`	Failure	Failure	Skip	Skip
13.29.E6	${\displaystyle{\displaystyle w(n)={\left(a\right)_{n}}U\left(n+a,b,z\right)}}$	`w(n)= pochhammer(a, n)KummerU(n + a, b, z)`	`w(n)= Pochhammer[a, n]HypergeometricU[n + a, b, z]`	Failure	Failure	Fail `1.520419005+1.650199040I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), w = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 1}` `2.873866917+2.939587822I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), w = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 2}` `4.267041895+4.298527135I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), w = 2^(1/2)+I2^(1/2), z = 2^(1/2)+I2^(1/2), n = 3}` `1.371726075+1.394092488I <- {a = 2^(1/2)+I2^(1/2), b = 2^(1/2)+I2^(1/2), w = 2^(1/2)+I2^(1/2), z = 2^(1/2)-I2^(1/2), n = 1}` ... skip entries to safe data	Skip
13.29.E7	${\displaystyle{\displaystyle z^{-a}=\sum_{s=0}^{\infty}\frac{{\left(a-b+1% \right)_{s}}}{s!}w(s)}}$	`(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}]`	Failure	Failure	Skip	Skip
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)* KummerU(a, 1 + a - b, z)= limit((A[n](z))/(B[n](z)), n = infinity)`	`(z)^(a)* HypergeometricU[a, 1 + a - b, z]= Limit[Divide[Subscript[A, n](z),Subscript[B, n](z)], n -> Infinity]`	Failure	Failure	Skip	Skip

Results of Confluent Hypergeometric Functions

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