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

TL;DR

This survey comprehensively explores the terminating basic hypergeometric representations and transformations of Askey-Wilson polynomials, highlighting their symmetry properties and exhaustive transformation formulas.

Contribution

It provides a complete classification of terminating hypergeometric representations and transformations for Askey-Wilson polynomials, emphasizing their symmetry-based derivations.

Findings

Exhaustive list of terminating hypergeometric representations

Complete set of transformation formulas for Askey-Wilson polynomials

Symmetry properties enable comprehensive exploration

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.