Hahn Polynomial

The orthogonal polynomials defined by

(1)

where  is the Pochhammer symbol and  is a generalized hypergeometric function (Koepf 1998). The first few are given by

			(2)
			(3)

Koekoek and Swarttouw (1998) define another Hahn polynomial

(4)

the dual Hahn polynomial

(5)

the continuous Hahn polynomial

(6)

and the continuous dual Hahn polynomial

(7)

for , 1, ..., , and where

(8)

REFERENCES:

Koekoek, R. and Swarttouw, R. F. "Continuous Dual Hahn," "Continuous Hahn," "Hahn," and "Dual Hahn." §1.3-1.6 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. 29-36, 1998.

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