Symmetry of terminating basic hypergeometric series representations of the Askey–Wilson polynomials

Published

August 10, 2022

Author(s)

Howard Cohl, Roberto S. Costas-Santos

Abstract

In this paper, we explore the symmetric nature of the terminating basic hypergeometric series representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. In particular we identify and classify the set of 4 and 7 equivalence classes of terminating balanced 4φ3 and terminating very-well-poised 8W7 basic hypergeometric series which are connected with the Askey–Wilson polynomials. We study the inversion properties of these equivalence classes and also identify the connection of both sets of equivalence classes with the symmetric group S6, the symmetry group of the terminating balanced 4φ3 . We then use terminating balanced 4φ3 and terminating very-well poised 8W7 transformations to give a broader interpretation of Watson's q-analog of Whipple's theorem and its converse.

Citation

Journal of Mathematical Analysis and Applications

Volume

517

Issue

1

Pub Type

Journals

Download Paper

DOI Link

Keywords

Basic hypergeometric series, Basic hypergeometric orthogonal polynomials, Basic hypergeometric transformations

Citation

Cohl, H. and Costas-Santos, R. (2022), Symmetry of terminating basic hypergeometric series representations of the Askey–Wilson polynomials, Journal of Mathematical Analysis and Applications, [online], https://doi.org/10.1016/j.jmaa.2022.126583 (Accessed October 14, 2025)