A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials

Victor J W Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.

Original languageEnglish
Pages (from-to)2003-2015
Number of pages13
JournalProceedings of the American Mathematical Society
Volume143
Issue number5
DOIs
Publication statusPublished - 2015
Externally publishedYes

Fingerprint

Quadratic equation solution
Askey-Wilson Polynomials
Basic Hypergeometric Series
Polynomials
Determinant
Sum formula
Interpolation
Pfaffian
Interpolate
Moment

Keywords

  • Askey-Wilson polynomials
  • Desnanot–Jacobi adjoint matrix theorem
  • Gram determinants
  • Moments of Askey-Wilson polynomials
  • Pfaffians
  • Quadratic formula of basic hypergeometric series

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials. / Guo, Victor J W; Ishikawa, Masao; Tagawa, Hiroyuki; Zeng, Jiang.

In: Proceedings of the American Mathematical Society, Vol. 143, No. 5, 2015, p. 2003-2015.

Research output: Contribution to journalArticle

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