Bootstrapping and Askey-Wilson polynomials

Jang Soo Kim, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.

Original languageEnglish (US)
Pages (from-to)501-520
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume421
Issue number1
DOIs
StatePublished - Jan 1 2015

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 National Science Foundation grant DMS-1148634 .

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

  • Askey-Wilson polynomials
  • Hermite polynomials
  • Moments
  • Orthogonal polynomials

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