Title

Functions of the second kind for classical polynomials

Authors

Authors

M. E. H. Ismail;Z. S. I. Mansour

Comments

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Abbreviated Journal Title

Adv. Appl. Math.

Keywords

Raising and lowering operators; Rodrigues formulas; Askey-Wilson; operator; Wilson operator; Jackson q-difference operator; Big and small; q-Jacobi polynomial; Al-Salam-Chihara polynomials; Indeterminate moment; problems; ORTHOGONAL POLYNOMIALS; DIFFERENCE-EQUATIONS; WILSON POLYNOMIALS; Mathematics, Applied

Abstract

We give new derivations of properties of the functions of the second kind of the Jacobi, little and big q-Jacobi polynomials, and the symmetric Al-Salam Chihara polynomials for q> 1. We also study the Askey Wilson functions and the Wilson functions of second kind. An integration by parts formula is derived for the Wilson operator in appropriate Hilbert space. In case of undetermined moment problem, we prove that the function of second kind depends on the measure. (C) 2013 Elsevier Inc. All rights reserved.

Journal Title

Advances in Applied Mathematics

Volume

54

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

66

Last Page

104

WOS Identifier

WOS:000332427700004

ISSN

0196-8858

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