Structure relations for monic orthogonal polynomials in two discrete variables

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:340

Article

Rodal, J.²  Area, I.²  Godoy, E.¹ 

[1] Univ Vigo, Dept Matemat Aplicada 2, ETS Ingn Ind, Vigo 36310, Spain

[2] Univ Vigo, Dept Matemat Aplicada 2, ETSE Telecomunicac, Vigo 36310, Spain

关键词: second order linear partial difference equation;    hypergeometric equation;    structure relation;    Hahn polynomials;    Kravchuk polynomials;    raising and lowering operators;   

DOI  :  10.1016/j.jmaa.2007.09.003

来源: Elsevier

【 摘 要 】

In this paper, extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given, by using an appropriate vector-matrix notation. Three-term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type. Structure relations, difference representations as well as lowering and raising operators are obtained. Finally, expressions for all matrix coefficients appearing in these finite-type relations are explicitly presented for a finite set of Hahn and Kravchuk orthogonal polynomials. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free