A characterization of an Askey-Wilson difference equation

Daniel J. Galiffa, Boon W. Ong

Research output: Contribution to journalArticle

Abstract

We determine the q-orthogonal polynomial solutions to the difference equation DqPn(X) = γnPn-1(X), where Dq is the Askey-Wilson divided-difference operator, using an approach that does not appear in the literature. To accomplish this, we construct a polynomial expansion via a Chebyshev basis, which ultimately allows explicit formulas to be derived for the recurrence coefficients of Pn(X) above. From there, we obtain our solutions and discuss some future research.

Original languageEnglish (US)
Pages (from-to)1372-1381
Number of pages10
JournalJournal of Difference Equations and Applications
Volume20
Issue number9
DOIs
StatePublished - Sep 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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