18.19

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.19.E1	${\displaystyle{\displaystyle p_{n}(x)=p_{n}\left(x;a,b,\overline{a},\overline{b}\right)}}$ p_{n}(x) = \contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}}		Error	Subscript[p, n][x] == I^(n)*Divide[Pochhammer[a + Conjugate[a], n]*Pochhammer[a + Conjugate[b], n], (n)!] * HypergeometricPFQ[{-(n), n + 2*Re[a + b] - 1, a + I*(x)}, {a + Conjugate[a], a + Conjugate[b]}, 1]	Missing Macro Error	Missing Macro Error	-	-
18.19.E2	${\displaystyle{\displaystyle w(z;a,b,\overline{a},\overline{b})=\Gamma\left(a+iz\right)\Gamma\left(b+iz\right)\Gamma\left(\overline{a}-iz\right)\Gamma\left(\overline{b}-iz\right)}}$ w(z;a,b,\conj{a},\conj{b}) = \EulerGamma@{a+iz}\EulerGamma@{b+iz}\EulerGamma@{\conj{a}-iz}\EulerGamma@{\conj{b}-iz}		w(z ; a , b , conjugate(a), conjugate(b)) = GAMMA(a + I*z)*GAMMA(b + I*z)*GAMMA(conjugate(a)- I*z)*GAMMA(conjugate(b)- I*z)	w[z ; a , b , Conjugate[a], Conjugate[b]] == Gamma[a + I*z]*Gamma[b + I*z]*Gamma[Conjugate[a]- I*z]*Gamma[Conjugate[b]- I*z]	Translation Error	Translation Error	-	-
18.19.E3	${\displaystyle{\displaystyle w(x)=w(x;a,b,\overline{a},\overline{b})}}$ w(x) = w(x;a,b,\conj{a},\conj{b})		w(x) = w(x ; a , b , conjugate(a), conjugate(b))	w[x] == w[x ; a , b , Conjugate[a], Conjugate[b]]	Translation Error	Translation Error	-	-
18.19.E3	${\displaystyle{\displaystyle w(x;a,b,\overline{a},\overline{b})=|\Gamma\left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)|^{2}}}$ w(x;a,b,\conj{a},\conj{b}) = |\EulerGamma@{a+\iunit x}\EulerGamma@{b+\iunit x}|^{2}	${\displaystyle{\displaystyle\Re(a+\mathrm{i}x)>0,\Re(b+\mathrm{i}x)>0}}$	w(x ; a , b , conjugate(a), conjugate(b)) = (abs(GAMMA(a + I*x)*GAMMA(b + I*x)))^(2)	w[x ; a , b , Conjugate[a], Conjugate[b]] == (Abs[Gamma[a + I*x]*Gamma[b + I*x]])^(2)	Translation Error	Translation Error	-	-
18.19.E5	${\displaystyle{\displaystyle k_{n}=\frac{{\left(n+2\Re\left(a+b\right)-1\right)_{n}}}{n!}}}$ k_{n} = \frac{\Pochhammersym{n+2\realpart@{a+b}-1}{n}}{n!}		k[n] = (pochhammer(n + 2*Re(a + b)- 1, n))/(factorial(n))	Subscript[k, n] == Divide[Pochhammer[n + 2*Re[a + b]- 1, n],(n)!]	Failure	Failure	Failed [298 / 300] Result: 6.866025404+.5000000000*I Test Values: {a = -3/2, b = -3/2, k[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -9.133974596+.5000000000*I Test Values: {a = -3/2, b = -3/2, k[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [298 / 300] Result: Complex[6.866025403784438, 0.49999999999999994] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-9.13397459621556, 0.49999999999999994] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
18.19.E7	${\displaystyle{\displaystyle w^{(\lambda)}(z;\phi)=\Gamma\left(\lambda+iz\right)\Gamma\left(\lambda-iz\right)e^{(2\phi-\pi)z}}}$ w^{(\lambda)}(z;\phi) = \EulerGamma@{\lambda+iz}\EulerGamma@{\lambda-iz}e^{(2\phi-\pi)z}	${\displaystyle{\displaystyle\Re(\lambda+\mathrm{i}z)>0,\Re(\lambda-\mathrm{i}z)>0}}$	(w(z ; phi))^(lambda) = GAMMA(lambda + I*z)*GAMMA(lambda - I*z)*exp((2*phi - Pi)*z)	(w[z ; \[Phi]])^(\[Lambda]) == Gamma[\[Lambda]+ I*z]*Gamma[\[Lambda]- I*z]*Exp[(2*\[Phi]- Pi)*z]	Translation Error	Translation Error	-	-
18.19.E8	${\displaystyle{\displaystyle w(x)=w^{(\lambda)}(x;\phi)}}$ w(x) = w^{(\lambda)}(x;\phi)	${\displaystyle{\displaystyle\lambda>0,0<\phi,\phi<\pi}}$	w(x) = (w(x ; phi))^(lambda)	w[x] == (w[x ; \[Phi]])^(\[Lambda])	Translation Error	Translation Error	-	-
18.19.E8	${\displaystyle{\displaystyle w^{(\lambda)}(x;\phi)=\left|\Gamma\left(\lambda+\mathrm{i}x\right)\right|^{2}e^{(2\phi-\pi)x}}}$ w^{(\lambda)}(x;\phi) = \left|\EulerGamma@{\lambda+\iunit x}\right|^{2}e^{(2\phi-\pi)x}	${\displaystyle{\displaystyle\lambda>0,0<\phi,\phi<\pi,\Re(\lambda+\mathrm{i}x)>0}}$	(w(x ; phi))^(lambda) = (abs(GAMMA(lambda + I*x)))^(2)* exp((2*phi - Pi)*x)	(w[x ; \[Phi]])^(\[Lambda]) == (Abs[Gamma[\[Lambda]+ I*x]])^(2)* Exp[(2*\[Phi]- Pi)*x]	Translation Error	Translation Error	-	-
18.19#Ex2	${\displaystyle{\displaystyle k_{n}=\frac{(2\sin\phi)^{n}}{n!}}}$ k_{n} = \frac{(2\sin@@{\phi})^{n}}{n!}		k[n] = ((2*sin(phi))^(n))/(factorial(n))	Subscript[k, n] == Divide[(2*Sin[\[Phi]])^(n),(n)!]	Failure	Failure	Failed [300 / 300] Result: -.8519352650-.1751929262*I Test Values: {phi = 1/2*3^(1/2)+1/2*I, k[n] = 1/2*3^(1/2)+1/2*I, n = 1} Result: -.3817262820-.6599548910*I Test Values: {phi = 1/2*3^(1/2)+1/2*I, k[n] = 1/2*3^(1/2)+1/2*I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.851935264815837, -0.17519292644574008] Test Values: {Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.3817262816831334, -0.6599548913509004] Test Values: {Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data