Two variable extensions of the Laguerre and disc polynomials

    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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