Divided difference operators and classical orthogonal polynomials. (English) Zbl 0696.33008
The divided difference operator introduced by R. Askey and J. Wilson [Mem. Am. Math. Soc. 319, 55 p. (1985; Zbl 0572.33012)] plays the same role for the \({}_ 4\phi_ 3\) orthogonal polynomials that the derivative does for Jacobi polynomials. This article gives a nice derivation of the connection coefficient result of L. J. Rogers [Proc. Lond. Math. Soc. 26, 15-32 (1895)] using this divided difference operator.
Reviewer: E.G.Kalnins
MSC:
33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
33E99 | Other special functions |