Orthogonal Polynomials - 18.20 Hahn Class: Explicit Representations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.20.E8	${\displaystyle{\displaystyle C_{n}\left(x;a\right)={{}_{2}F_{0}}\left({-n,-x\atop-};-a^{-1}\right)}}$ \CharlierpolyC{n}@{x}{a} = \genhyperF{2}{0}@@{-n,-x}{-}{-a^{-1}}		Error	HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{- n , - x}, {-}, - (a)^(- 1)]	Missing Macro Error	Missing Macro Error	-	-
18.20.E9	${\displaystyle{\displaystyle p_{n}\left(x;a,b,\overline{a},\overline{b}\right)=\frac{{\mathrm{i}^{n}}{\left(a+\overline{a}\right)_{n}}{\left(a+\overline{b}\right)_{n}}}{n!}\*{{}_{3}F_{2}}\left({-n,n+2\Re\left(a+b\right)-1,a+\mathrm{i}x\atop a+\overline{a},a+\overline{b}};1\right)}}$ \contHahnpolyp{n}@{x}{a}{b}{\conj{a}}{\conj{b}} = \frac{\iunit^{n}\Pochhammersym{a+\conj{a}}{n}\Pochhammersym{a+\conj{b}}{n}}{n!}\*\genhyperF{3}{2}@@{-n,n+2\realpart@{a+b}-1,a+\iunit x}{a+\conj{a},a+\conj{b}}{1}		Error	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] == Divide[(I)^(n)* 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	-	-