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Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials.

Howard S Cohl1, Roberto S Costas-Santos2, Linus Ge3

  • 1Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USA.

Symmetry
|May 9, 2022
PubMed
Summary
This summary is machine-generated.

This paper surveys terminating basic hypergeometric representations of Askey-Wilson polynomials. It details the specific hypergeometric transformations these polynomials satisfy.

Keywords:
basic hypergeometric orthogonal polynomialsbasic hypergeometric seriesbasic hypergeometric transformations

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Area of Science:

  • Mathematics
  • Special Functions
  • Combinatorics

Background:

  • Askey-Wilson polynomials are a significant family of orthogonal polynomials.
  • Basic hypergeometric series and identities are fundamental in combinatorics and mathematical physics.

Purpose of the Study:

  • To provide a comprehensive survey of terminating basic hypergeometric representations.
  • To identify and analyze the basic hypergeometric transformations satisfied by Askey-Wilson polynomials.

Main Methods:

  • Systematic exploration of known results and techniques.
  • Analysis of polynomial properties within the framework of basic hypergeometric series.

Main Results:

  • Detailed characterization of terminating basic hypergeometric representations for Askey-Wilson polynomials.
  • Identification of a comprehensive set of basic hypergeometric transformations governing these polynomials.

Conclusions:

  • The study consolidates understanding of Askey-Wilson polynomials in the context of basic hypergeometric functions.
  • This work serves as a valuable reference for researchers in special functions and related fields.