A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials
Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng
TL;DR
This paper introduces a quadratic formula for basic hypergeometric series that simplifies proofs of determinant and Pfaffian formulas, and connects to Askey-Wilson polynomials and their moments.
Contribution
It presents a new quadratic formula for basic hypergeometric series, linking it to Askey-Wilson polynomials and providing streamlined proofs of related formulas.
Findings
Derived a general quadratic formula for basic hypergeometric series
Connected the quadratic formula to a Gram determinant formula for Askey-Wilson polynomials
Reproduced a double-sum formula for Askey-Wilson moments using Newton's interpolation
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.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Iterative Methods for Nonlinear Equations