Characterization of the Dunkl-classical symmetric orthogonal polynomials

被引：39

作者：

Ben Cheikh, Y. ^{[1
]}

Gaied, M.

机构：

[1] Fac Sci Monastir, Dept Math, Monastir 5019, Tunisia

[2] Inst Preparatoire Etud Ingn, Dept Preparat Math Phys, Monastir 5019, Tunisia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 187卷 / 01期

关键词：

orthogonal polynomials; symmetric orthogonal polynomials; Dunkl operator; generalized hermite polynomials; generalized Gegenbauer polynomials; sieved ultraspherical polynomials;

D O I：

10.1016/j.amc.2006.08.108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the notion of Dunk1-classical orthogonal polynomials. Then, we show that generalized Hermite and generalized Gegenbauer polynomials are the only Dunk1-classical symmetric orthogonal polynomials by solving a suitable differential-difference equation. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：105 / 114

页数：10

共 19 条

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Abdelkarim F., 1997, Results Math, V32, P1

[2]

[Anonymous], SPECIAL FUNCTIONS MA

[3] Classical symmetric orthogonal polynomials of a discrete variable [J].