Moments of askey-wilson polynomials

Jang Soo Kim, Dennis W Stanton

Research output: Contribution to journalConference articlepeer-review

1 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)169-180
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2013
Event25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France
Duration: Jun 24 2013Jun 28 2013

Bibliographical note

Funding Information:
The first author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2013R1A1A2061006 ). The second author was supported by NSF Grant DMS-1148634 .

Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

Keywords

  • Askey-wilson polynomials
  • Hypergeometric series
  • Moments of orthogonal polynomials
  • Motzkin paths

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