Title

Connection relations and characterizations of orthogonal polynomials

Authors

Authors

M. E. H. Ismail;P. Simeonov

Comments

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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

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