English

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

Combinatorics 2013-08-13 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.1212.1887,
  title  = {A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials},
  author = {Victor J. W. Guo and Masao Ishikawa and Hiroyuki Tagawa and Jiang Zeng},
  journal= {arXiv preprint arXiv:1212.1887},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-21T22:51:05.225Z