Moments of Askey-Wilson polynomials

Jang Soo Kim, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

New formulas for the nth moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.

Original languageEnglish (US)
Pages (from-to)113-145
Number of pages33
JournalJournal of Combinatorial Theory. Series A
Volume125
Issue number1
DOIs
StatePublished - Jul 2014

Keywords

  • Askey-Wilson polynomials
  • Matchings
  • Moments of orthogonal polynomials
  • Motzkin paths
  • Staircase tableaux

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