Expansions In The Askey-Wilson Polynomials

Keywords

Andrews formula; Askey-Wilson polynomials; Basic hypergeometric series; Expansion formulas; Generating functions

Abstract

We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials.

Publication Date

4-1-2015

Publication Title

Journal of Mathematical Analysis and Applications

Volume

424

Issue

1

Number of Pages

664-674

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2014.11.048

Socpus ID

84920605456 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84920605456

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