Orthogonal Polynomials - 18.21 Hahn Class: Interrelations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.21#Ex3	${\displaystyle{\displaystyle C_{n}\left(x;a\right)=C_{x}\left(n;a\right)}}$ \CharlierpolyC{n}@{x}{a} = \CharlierpolyC{x}@{n}{a}		Error	HypergeometricPFQ[{-(n), -(x)}, {}, -Divide[1,a]] == HypergeometricPFQ[{-(x), -(n)}, {}, -Divide[1,a]]	Missing Macro Error	Missing Macro Error	-	-
18.21.E9	${\displaystyle{\displaystyle\lim_{a\to\infty}(2a)^{\frac{1}{2}n}C_{n}\left((2a)^{\frac{1}{2}}x+a;a\right)=(-1)^{n}H_{n}\left(x\right)}}$ \lim_{a\to\infty}(2a)^{\frac{1}{2}n}\CharlierpolyC{n}@{(2a)^{\frac{1}{2}}x+a}{a} = (-1)^{n}\HermitepolyH{n}@{x}		Error	Limit[(2*a)^(Divide[1,2]*n)* HypergeometricPFQ[{-(n), -((2*a)^(Divide[1,2])* x + a)}, {}, -Divide[1,a]], a -> Infinity, GenerateConditions->None] == (- 1)^(n)* HermiteH[n, x]	Missing Macro Error	Missing Macro Error	-	-