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2 - A Brief Review of q-Series

Published online by Cambridge University Press:  07 October 2020

By
Mourad E.H. Ismail
Edited by
Howard S. Cohl  and
Mourad E. H. Ismail
Howard S. Cohl
Affiliation:
National Institute of Standards and Technology
Mourad E. H. Ismail
Affiliation:
University of Central Florida
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Summary

We sample certain results from the theory of q-series, including summation and transformation formulas, as well as some recent results which are not available in book form. Our approach is systematic and uses the Askey–Wilson calculus and Rodrigues-type formulas.

Keywords

q-seriesAskey–Wilson calculusbasic hypergeometric functionsorthogonal polynomialsq-Taylor seriesladder operatorsRodriqgues-type formulasbasic hypergeometric transformationsbasic hypergeometric summation
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Chapter
Information
Lectures on Orthogonal Polynomials and Special Functions , pp. 76 - 130
Publisher: Cambridge University Press
Print publication year: 2020

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