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

Victor J.W. Guo; Masao Ishikawa; Hiroyuki Tagawa; Jiang Zeng

doi:10.1090/S0002-9939-2015-12099-0

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 journal › Article › peer-review

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 language	English
Pages (from-to)	2003-2015
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-2015-12099-0
Publication status	Published - 2015

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

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AU - Guo, Victor J.W.

AU - Ishikawa, Masao

AU - Tagawa, Hiroyuki

AU - Zeng, Jiang

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Y1 - 2015

N2 - 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.

AB - 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.

KW - Askey-Wilson polynomials

KW - Desnanot–Jacobi adjoint matrix theorem

KW - Gram determinants

KW - Moments of Askey-Wilson polynomials

KW - Pfaffians

KW - Quadratic formula of basic hypergeometric series

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