Title

Functions Of The Second Kind For Classical Polynomials

Keywords

Al-Salam-Chihara polynomials; Askey-Wilson operator; Big and small q-Jacobi polynomial; Indeterminate moment problems; Jackson q-difference operator; Raising and lowering operators; Rodrigues formulas; Wilson operator

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. © 2013 Elsevier Inc.

Publication Date

3-1-2014

Publication Title

Advances in Applied Mathematics

Volume

54

Issue

1

Number of Pages

66-104

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.aam.2013.11.002

Socpus ID

84894090932 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84894090932

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