Title

A Moment Problem And A Family Of Integral Evaluations

Keywords

Al-Salam-Chihara polynomials; Bethe Ansatz equations; Biorthogonal rational functions; Divided difference operators; Indeterminate moment problems; Integral operators; q -Hermite polynomials -1; Raising and lowering operators

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. © 2005 American Mathematical Society.

Publication Date

9-1-2006

Publication Title

Transactions of the American Mathematical Society

Volume

358

Issue

9

Number of Pages

4071-4097

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9947-05-03785-2

Socpus ID

33748286736 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33748286736

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