Two variable extensions of the Laguerre and disc polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Ismail, Mourad E. H.^1,2  Zeng, Jiang³ 

[1] King Saud Univ, Dept Math, Riyadh, Saudi Arabia

[2] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[3] Univ Lyon 1, CNRS, Inst Camille Jordan, UMR 5208, F-69622 Villeurbanne, France

关键词: 2D-Laguerre polynomials;    (Zernike) disc polynomials;    Integrals of products of orthogonal;    polynomials Generating functions;    Connection relations;    Combinatorial interpretations;   

DOI  :  10.1016/j.jmaa.2014.11.015

来源: Elsevier

【 摘 要 】

This work contains a detailed study of a one parameter generalization of the 2D-Hermite polynomials and a two parameter extension of Zernike's disc polynomials. We derive linear and bilinear generating functions, and explicit formulas for our generalizations and study integrals of products of some of these 2D orthogonal polynomials. We also establish a combinatorial inequality involving elementary symmetric functions and solve the connection coefficient problem for our polynomials. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free