Connection relations and characterizations of orthogonal polynomials

    Authors

    M. E. H. Ismail;P. Simeonov

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Adv. Appl. Math.

    Keywords

    Askey-Wilson polynomials; Wilson polynomials; Al-Salam-Chihara; polynomials; Jacobi polynomials; Meixner-Pollaczek polynomials; Recurrence relations; Characterizations; Connection relations; SERIES; COEFFICIENTS; Mathematics, Applied

    Abstract

    We give a general method of characterizing symmetric orthogonal polynomials through a certain type of connection relations. This method is applied to Al-Salam-Chihara. Askey-Wilson, and Meixner-Pollaczek polynomials. This characterization technique unifies and extends some previous characterization results of Lasser and Obermaier and Ismail and Obermaier. Along the way we explicitly evaluate the connection coefficients in the expansion of D(q)(2)p(n) in terms of (P-k), where D-q is the Askey-Wilson operator and {P-k} are general Askey-Wilson polynomials. As a limiting case we derive the corresponding connection coefficients in the expansion of (WWn)-W-2 in terms of {W-k}, where W is the Wilson operator and {W-k} are general Wilson polynomials. Using the connection relation for Askey-Wilson polynomials, we obtain a characterization for the two-parameter symmetric Askey-Wilson polynomials. The connection relations between D-m P-n((alpha,beta)), D := d/dx and {P-k((alpha,beta))} are also derived. (c) 2012 Elsevier Inc. All rights reserved.

    Journal Title

    Advances in Applied Mathematics

    Volume

    49

    Issue/Number

    2

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    134

    Last Page

    164

    WOS Identifier

    WOS:000307147200004

    ISSN

    0196-8858

    Share

    COinS