Expansions in the Askey-Wilson polynomials

Mourad E.H. Ismail, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

3 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 languageEnglish (US)
Pages (from-to)664-674
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume424
Issue number1
DOIs
StatePublished - 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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