Charlier Polynomial -- from Wolfram MathWorld

Calculus and Analysis > Special Functions > Orthogonal Polynomials >

Charlier Polynomial

The orthogonal polynomials defined by

			(1)
			(2)
			(3)
			(4)

where is the Pochhammer symbol (Koekoek and Swarttouw 1998). The first few are given by

			(5)
			(6)
			(7)

REFERENCES:

Koekoek, R. and Swarttouw, R. F. "Charlier." §1.12 in The Askey-Scheme of Hypergeometric Orthogonal Polynomials and its -Analogue. Delft, Netherlands: Technische Universiteit Delft, Faculty of Technical Mathematics and Informatics Report 98-17, pp. 49-50, 1998.

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 115, 1998.

CITE THIS AS:

Weisstein, Eric W. "Charlier Polynomial." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CharlierPolynomial.html