Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials

Abstract

In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey-Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. From the terminating basic hypergeometric representations of these polynomials, and due to symmetry in their free parameters, we are able to exhaustively explore the terminating basic hypergeometric transformation formulae which these polynomials satisfy.

arXiv comment14 pages

References in corpus (2)

• Additions to the formula lists in "Hypergeometric orthogonal polynomials and their $q$-analogues" by Koekoek, Lesky and Swarttouw
• Symmetry Groups of $A_n$ Hypergeometric Series

Cited by in corpus (1)

• Utility of integral representations for basic hypergeometric functions and orthogonal polynomials