Expansion of analytic functions in q-orthogonal polynomials

Moritz Simon, Sergei Suslov

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey-Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.

Original languageEnglish (US)
Pages (from-to)281-303
Number of pages23
JournalRamanujan Journal
Volume19
Issue number3
DOIs
StatePublished - Jan 1 2009

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Keywords

  • Al-Salam and Chihara polynomials
  • Askey-Wilson polynomials
  • Basic hypergeometric functions
  • Chebyshev polynomials
  • Continuous big q-Hermite polynomials
  • Continuous dual q-Hahn polynomials
  • Continuous q-Hermite polynomials
  • Continuous q-Jacobi polynomials
  • Continuous q-ultraspherical polynomials
  • Jacobi polynomials
  • q-orthogonal polynomials

ASJC Scopus subject areas

  • Algebra and Number Theory

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