Expansions in the Askey-Wilson polynomials

Mourad E.H. Ismail; Dennis Stanton

doi:10.1016/j.jmaa.2014.11.048

Expansions in the Askey-Wilson polynomials

Mourad E.H. Ismail, Dennis Stanton

Mathematics

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7 Scopus citations

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.

Original language	English (US)
Pages (from-to)	664-674
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	424
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.11.048
State	Published - Apr 1 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

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

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AB - 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.

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KW - Basic hypergeometric series

KW - Expansion formulas

KW - Generating functions

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Expansions in the Askey-Wilson polynomials

Abstract

Bibliographical note

Keywords

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