Title

Two variable extensions of the Laguerre and disc polynomials

Authors

Authors

M. E. H. Ismail;J. Zeng

Comments

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Abbreviated Journal Title

J. Math. Anal. Appl.

Keywords

2D-Laguerre polynomials; (Zernike) disc polynomials; Integrals of; products of orthogonal; polynomials Generating functions; Connection; relations; Combinatorial interpretations; ORTHOGONAL POLYNOMIALS; ZERNIKE; Mathematics, Applied; Mathematics

Abstract

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.

Journal Title

Journal of Mathematical Analysis and Applications

Volume

424

Issue/Number

1

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

289

Last Page

303

WOS Identifier

WOS:000348488700015

ISSN

0022-247X

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