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On the Askey-Wilson and Rogers Polynomials

Published online by Cambridge University Press:  20 November 2018

Mourad E. H. Ismail  and
Dennis Stanton
Mourad E. H. Ismail
Affiliation:
Arizona State University, Tempe, Arizona
Dennis Stanton
Affiliation:
University of Minnesota, Minneapolis, Minnesota
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The q-shifted factorial (a)n or (a; q)n is

and an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials

1.1

where

1.2

and

1.3

We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [2].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1025 - 1045
Copyright
Copyright © Canadian Mathematical Society 1988

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