Title

A moment problem and a family of integral evaluations

Authors

Authors

J. S. Christiansen;M. E. H. Ismail

Comments

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Abbreviated Journal Title

Trans. Am. Math. Soc.

Keywords

indeterminate moment problems; q(-1)-hermite polynomials; Al-Salam-Chihara polynomials; biorthogonal rational functions; divided; difference operators; raising and lowering operators; Bethe Ansatz; equations; integral operators; CLASSICAL ORTHOGONAL POLYNOMIALS; ASKEY-WILSON OPERATOR; Q-HERMITE; POLYNOMIALS; Q-BETA-INTEGRALS; INVERSE; Mathematics

Abstract

We study the Al-Salam-Chihara polynomials when q > 1. Several solutions of the associated moment problem are found, and the orthogonality relations lead to explicit evaluations of several integrals. The polynomials are shown to have raising and lowering operators and a second order operator equation of Sturm-Liouville type whose eigenvalues are found explicitly. We also derive new measures with respect to which the Ismail-Masson system of rational functions is biorthogonal. An integral representation of the right inverse of a divided difference operator is also obtained.

Journal Title

Transactions of the American Mathematical Society

Volume

358

Issue/Number

9

Publication Date

1-1-2006

Document Type

Article

Language

English

First Page

4071

Last Page

4097

WOS Identifier

WOS:000238321800014

ISSN

0002-9947

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