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

2012/12/09 by Victor J. W. Guo, Masao Ishikawa, Guo, Victor J. W. +5 · 1 citation
Mathematics · #33D45 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Primary 33C45 #Secondary 05A19 #math.CA #math.CO #msc:05A19 #msc:33C45 #msc:33D45

paper · pdf · doi:10.48550/arxiv.1212.1887

12 pages, to appear in Proceedings of the American Mathmatical Society

openalex publication_date 2012/12/09 · arxiv created 2013/08/12 · arxiv updated 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Evaluation of terminating and non-terminating sums containing the digamma function

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