13.6

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.6.E1	${\displaystyle{\displaystyle M\left(a,a,z\right)=e^{z}}}$ \KummerconfhyperM@{a}{a}{z} = e^{z}		KummerM(a, a, z) = exp(z)	Hypergeometric1F1[a, a, z] == Exp[z]	Successful	Successful	-	Successful [Tested: 42]
13.6.E2	${\displaystyle{\displaystyle M\left(1,2,2z\right)=\frac{e^{z}}{z}\sinh z}}$ \KummerconfhyperM@{1}{2}{2z} = \frac{e^{z}}{z}\sinh@@{z}		KummerM(1, 2, 2*z) = (exp(z))/(z)*sinh(z)	Hypergeometric1F1[1, 2, 2*z] == Divide[Exp[z],z]*Sinh[z]	Successful	Successful	-	Successful [Tested: 7]
13.6.E3	${\displaystyle{\displaystyle M\left(0,b,z\right)=U\left(0,b,z\right)}}$ \KummerconfhyperM@{0}{b}{z} = \KummerconfhyperU@{0}{b}{z}		KummerM(0, b, z) = KummerU(0, b, z)	Hypergeometric1F1[0, b, z] == HypergeometricU[0, b, z]	Successful	Successful	-	Successful [Tested: 42]
13.6.E3	${\displaystyle{\displaystyle U\left(0,b,z\right)=1}}$ \KummerconfhyperU@{0}{b}{z} = 1		KummerU(0, b, z) = 1	HypergeometricU[0, b, z] == 1	Successful	Successful	-	Successful [Tested: 42]
13.6.E4	${\displaystyle{\displaystyle U\left(a,a+1,z\right)=z^{-a}}}$ \KummerconfhyperU@{a}{a+1}{z} = z^{-a}		KummerU(a, a + 1, z) = (z)^(- a)	HypergeometricU[a, a + 1, z] == (z)^(- a)	Failure	Successful	Successful [Tested: 42]	Successful [Tested: 42]
13.6.E5	${\displaystyle{\displaystyle M\left(a,a+1,-z\right)=e^{-z}M\left(1,a+1,z\right)}}$ \KummerconfhyperM@{a}{a+1}{-z} = e^{-z}\KummerconfhyperM@{1}{a+1}{z}		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	Skip - symbolical successful subtest	Failed [7 / 42] Result: Indeterminate Test Values: {Rule[a, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Indeterminate Test Values: {Rule[a, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.6.E5	${\displaystyle{\displaystyle e^{-z}M\left(1,a+1,z\right)=az^{-a}\gamma\left(a,z\right)}}$ e^{-z}\KummerconfhyperM@{1}{a+1}{z} = az^{-a}\incgamma@{a}{z}	${\displaystyle{\displaystyle\Re a>0}}$	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	Failed [21 / 21] Result: .1786149082+.5798847761*I Test Values: {a = 3/2, z = 1/2*3^(1/2)+1/2*I} Result: 4.103691021-1.156198608*I Test Values: {a = 3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Successful [Tested: 21]
13.6.E6	${\displaystyle{\displaystyle U\left(a,a,z\right)=z^{1-a}U\left(1,2-a,z\right)}}$ \KummerconfhyperU@{a}{a}{z} = z^{1-a}\KummerconfhyperU@{1}{2-a}{z}		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	-	Successful [Tested: 42]
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}\KummerconfhyperU@{1}{2-a}{z} = z^{1-a}e^{z}\genexpintE{a}@{z}		(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	-	Successful [Tested: 42]
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}e^{z}\genexpintE{a}@{z} = e^{z}\incGamma@{1-a}{z}		(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	-	Successful [Tested: 42]
13.6.E7	${\displaystyle{\displaystyle M\left(\tfrac{1}{2},\tfrac{3}{2},-z^{2}\right)=\frac{\sqrt{\pi}}{2z}\operatorname{erf}\left(z\right)}}$ \KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{\sqrt{\pi}}{2z}\erf@{z}		KummerM((1)/(2), (3)/(2), - (z)^(2)) = (sqrt(Pi))/(2*z)*erf(z)	Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] == Divide[Sqrt[Pi],2*z]*Erf[z]	Successful	Successful	-	Successful [Tested: 7]
13.6.E8	${\displaystyle{\displaystyle U\left(\tfrac{1}{2},\tfrac{1}{2},z^{2}\right)=\sqrt{\pi}e^{z^{2}}\operatorname{erfc}\left(z\right)}}$ \KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \sqrt{\pi}e^{z^{2}}\erfc@{z}		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	Failed [2 / 7] Result: .418096912e-1+2.795226389*I Test Values: {z = -1/2+1/2*I*3^(1/2)} Result: -2.288685714-4.974950146*I Test Values: {z = -1/2*3^(1/2)-1/2*I}	Failed [2 / 7] Result: Complex[0.041809690497868646, 2.7952263885381483] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[-2.28868571442365, -4.974950145988551] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.6.E9	${\displaystyle{\displaystyle M\left(\nu+\tfrac{1}{2},2\nu+1,2z\right)=\Gamma\left(1+\nu\right)e^{z}\left(\ifrac{z}{2}\right)^{-\nu}I_{\nu}\left(z\right)}}$ \KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{2z} = \EulerGamma@{1+\nu}e^{z}\left(\ifrac{z}{2}\right)^{-\nu}\modBesselI{\nu}@{z}	${\displaystyle{\displaystyle\Re(1+\nu)>0,\Re(\nu+k+1)>0}}$	KummerM(nu +(1)/(2), 2*nu + 1, 2*z) = GAMMA(1 + nu)*exp(z)*((z)/(2))^(- nu)* BesselI(nu, z)	Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, 2*z] == Gamma[1 + \[Nu]]*Exp[z]*(Divide[z,2])^(- \[Nu])* BesselI[\[Nu], z]	Successful	Successful	-	Failed [7 / 56] Result: Complex[-1.026957443693084, -2.3780953180269115] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]} Result: Complex[0.5295327248436391, -0.1815534052901876] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]} ... skip entries to safe data
13.6.E10	${\displaystyle{\displaystyle U\left(\nu+\tfrac{1}{2},2\nu+1,2z\right)=\frac{1}{\sqrt{\pi}}e^{z}\left(2z\right)^{-\nu}K_{\nu}\left(z\right)}}$ \KummerconfhyperU@{\nu+\tfrac{1}{2}}{2\nu+1}{2z} = \frac{1}{\sqrt{\pi}}e^{z}\left(2z\right)^{-\nu}\modBesselK{\nu}@{z}		KummerU(nu +(1)/(2), 2*nu + 1, 2*z) = (1)/(sqrt(Pi))*exp(z)*(2*z)^(- nu)* BesselK(nu, z)	HypergeometricU[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, 2*z] == Divide[1,Sqrt[Pi]]*Exp[z]*(2*z)^(- \[Nu])* BesselK[\[Nu], z]	Successful	Successful	-	Successful [Tested: 70]
13.6.E11	${\displaystyle{\displaystyle U\left(\tfrac{5}{6},\tfrac{5}{3},\tfrac{4}{3}z^{3/2}\right)=\sqrt{\pi}\frac{3^{5/6}\exp\left(\tfrac{2}{3}z^{3/2}\right)}{2^{2/3}z}\mathrm{Ai}\left(z\right)}}$ \KummerconfhyperU@{\tfrac{5}{6}}{\tfrac{5}{3}}{\tfrac{4}{3}z^{3/2}} = \sqrt{\pi}\frac{3^{5/6}\exp@{\tfrac{2}{3}z^{3/2}}}{2^{2/3}z}\AiryAi@{z}		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	Failed [1 / 7] Result: .7957982359-.7292249892*I Test Values: {z = -1/2*3^(1/2)-1/2*I}	Failed [1 / 7] Result: Complex[0.7957982355202466, -0.7292249896477329] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.6.E12	${\displaystyle{\displaystyle U\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a+\frac{1}{4}}e^{\frac{1}{4}z^{2}}U\left(a,z\right)}}$ \KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a+\frac{1}{4}}e^{\frac{1}{4}z^{2}}\paraU@{a}{z}		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[- 1/2 -(a), z]	Failure	Failure	Failed [10 / 42] Result: .7071067808-1.224744871*I Test Values: {a = -3/2, z = -1/2+1/2*I*3^(1/2)} Result: 1.224744871+.7071067810*I Test Values: {a = -3/2, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [10 / 42] Result: Complex[0.7071067811865475, -1.224744871391589] Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[1.224744871391589, 0.7071067811865475] Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data
13.6.E13	${\displaystyle{\displaystyle U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{\frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}}}{z}U\left(a,z\right)}}$ \KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}}}{z}\paraU@{a}{z}		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[- 1/2 -(a), z]	Failure	Failure	Failed [10 / 42] Result: 3.981039608+.280376847*I Test Values: {a = 3/2, z = -1/2+1/2*I*3^(1/2)} Result: 9.425210776+2.041008108*I Test Values: {a = 3/2, z = -1/2*3^(1/2)-1/2*I} ... skip entries to safe data	Failed [10 / 42] Result: Complex[3.9810396073031904, 0.2803768494018799] Test Values: {Rule[a, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[9.42521077642933, 2.0410081046172346] Test Values: {Rule[a, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]} ... skip entries to safe data
13.6.E14	${\displaystyle{\displaystyle M\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}z^{2}\right)=\frac{2^{\frac{1}{2}a-\frac{3}{4}}\Gamma\left(\tfrac{1}{2}a+\tfrac{3}{4}\right)e^{\frac{1}{4}z^{2}}}{\sqrt{\pi}}\*\left(U\left(a,z\right)+U\left(a,-z\right)\right)}}$ \KummerconfhyperM@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}} = \frac{2^{\frac{1}{2}a-\frac{3}{4}}\EulerGamma@{\tfrac{1}{2}a+\tfrac{3}{4}}e^{\frac{1}{4}z^{2}}}{\sqrt{\pi}}\*\left(\paraU@{a}{z}+\paraU@{a}{-z}\right)	${\displaystyle{\displaystyle\Re(\tfrac{1}{2}a+\tfrac{3}{4})>0}}$	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[- 1/2 -(a), z]+ ParabolicCylinderD[- 1/2 -(a), - z])	Successful	Successful	-	Successful [Tested: 28]
13.6.E15	${\displaystyle{\displaystyle M\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=\frac{2^{\frac{1}{2}a-\frac{5}{4}}\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{4}\right)e^{\frac{1}{4}z^{2}}}{z\sqrt{\pi}}\*\left(U\left(a,-z\right)-U\left(a,z\right)\right)}}$ \KummerconfhyperM@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = \frac{2^{\frac{1}{2}a-\frac{5}{4}}\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{4}}e^{\frac{1}{4}z^{2}}}{z\sqrt{\pi}}\*\left(\paraU@{a}{-z}-\paraU@{a}{z}\right)	${\displaystyle{\displaystyle\Re(\tfrac{1}{2}a+\tfrac{1}{4})>0}}$	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)))/(z*sqrt(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)],z*Sqrt[Pi]]*(ParabolicCylinderD[- 1/2 -(a), - z]- ParabolicCylinderD[- 1/2 -(a), z])	Successful	Successful	-	Successful [Tested: 21]
13.6.E16	${\displaystyle{\displaystyle M\left(-n,\tfrac{1}{2},z^{2}\right)=(-1)^{n}\frac{n!}{(2n)!}H_{2n}\left(z\right)}}$ \KummerconfhyperM@{-n}{\tfrac{1}{2}}{z^{2}} = (-1)^{n}\frac{n!}{(2n)!}\HermitepolyH{2n}@{z}		KummerM(- n, (1)/(2), (z)^(2)) = (- 1)^(n)*(factorial(n))/(factorial(2*n))*HermiteH(2*n, z)	Hypergeometric1F1[- n, Divide[1,2], (z)^(2)] == (- 1)^(n)*Divide[(n)!,(2*n)!]*HermiteH[2*n, z]	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
13.6.E17	${\displaystyle{\displaystyle M\left(-n,\tfrac{3}{2},z^{2}\right)=(-1)^{n}\frac{n!}{(2n+1)!2z}H_{2n+1}\left(z\right)}}$ \KummerconfhyperM@{-n}{\tfrac{3}{2}}{z^{2}} = (-1)^{n}\frac{n!}{(2n+1)!2z}\HermitepolyH{2n+1}@{z}		KummerM(- n, (3)/(2), (z)^(2)) = (- 1)^(n)*(factorial(n))/(factorial(2*n + 1)*2*z)*HermiteH(2*n + 1, z)	Hypergeometric1F1[- n, Divide[3,2], (z)^(2)] == (- 1)^(n)*Divide[(n)!,(2*n + 1)!*2*z]*HermiteH[2*n + 1, z]	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
13.6.E18	${\displaystyle{\displaystyle U\left(\tfrac{1}{2}-\tfrac{1}{2}n,\tfrac{3}{2},z^{2}\right)=2^{-n}z^{-1}H_{n}\left(z\right)}}$ \KummerconfhyperU@{\tfrac{1}{2}-\tfrac{1}{2}n}{\tfrac{3}{2}}{z^{2}} = 2^{-n}z^{-1}\HermitepolyH{n}@{z}		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	Failed [2 / 21] Result: .5000000003-2.598076212*I Test Values: {z = -1/2+1/2*I*3^(1/2), n = 2} Result: .8660254044+1.500000000*I Test Values: {z = -1/2*3^(1/2)-1/2*I, n = 2}	Failed [2 / 21] Result: Complex[0.5000000000000006, -2.5980762113533156] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[0.8660254037844388, 1.5] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
13.6.E19	${\displaystyle{\displaystyle U\left(-n,\alpha+1,z\right)=(-1)^{n}{\left(\alpha+1\right)_{n}}M\left(-n,\alpha+1,z\right)}}$ \KummerconfhyperU@{-n}{\alpha+1}{z} = (-1)^{n}\Pochhammersym{\alpha+1}{n}\KummerconfhyperM@{-n}{\alpha+1}{z}		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 [Tested: 63]	Successful [Tested: 63]
13.6.E19	${\displaystyle{\displaystyle(-1)^{n}{\left(\alpha+1\right)_{n}}M\left(-n,\alpha+1,z\right)=(-1)^{n}n!L^{(\alpha)}_{n}\left(z\right)}}$ (-1)^{n}\Pochhammersym{\alpha+1}{n}\KummerconfhyperM@{-n}{\alpha+1}{z} = (-1)^{n}n!\LaguerrepolyL[\alpha]{n}@{z}		(- 1)^(n)* pochhammer(alpha + 1, n)*KummerM(- n, alpha + 1, z) = (- 1)^(n)* factorial(n)*LaguerreL(n, alpha, z)	(- 1)^(n)* Pochhammer[\[Alpha]+ 1, n]*Hypergeometric1F1[- n, \[Alpha]+ 1, z] == (- 1)^(n)* (n)!*LaguerreL[n, \[Alpha], z]	Missing Macro Error	Successful	Skip - symbolical successful subtest	Successful [Tested: 63]
13.6.E20	${\displaystyle{\displaystyle U\left(-n,z-n+1,a\right)={\left(-z\right)_{n}}M\left(-n,z-n+1,a\right)}}$ \KummerconfhyperU@{-n}{z-n+1}{a} = \Pochhammersym{-z}{n}\KummerconfhyperM@{-n}{z-n+1}{a}		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	Error	Failed [6 / 126] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[n, 3], Rule[z, 2]} Result: Indeterminate Test Values: {Rule[a, 1.5], Rule[n, 3], Rule[z, 2]} ... skip entries to safe data
13.6.E20	${\displaystyle{\displaystyle{\left(-z\right)_{n}}M\left(-n,z-n+1,a\right)=a^{n}C_{n}\left(z;a\right)}}$ \Pochhammersym{-z}{n}\KummerconfhyperM@{-n}{z-n+1}{a} = a^{n}\CharlierpolyC{n}@{z}{a}		Error	Pochhammer[- z, n]*Hypergeometric1F1[- n, z - n + 1, a] == (a)^(n)* HypergeometricPFQ[{-(n), -(z)}, {}, -Divide[1,a]]	Missing Macro Error	Missing Macro Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
13.6.E21	${\displaystyle{\displaystyle U\left(a,b,z\right)=z^{-a}{{}_{2}F_{0}}\left(a,a-b+1;-;-z^{-1}\right)}}$ \KummerconfhyperU@{a}{b}{z} = z^{-a}\genhyperF{2}{0}@{a,a-b+1}{-}{-z^{-1}}		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