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q-Integral and Moment Representations for q-Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

Mourad E. H. Ismail  and
Dennis Stanton
Mourad E. H. Ismail
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700, U.S.A.
Dennis Stanton
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455 U.S.A.
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Abstract

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We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for $q$-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the $q$-exponential function $\text{ }{{\varepsilon }_{q}}$.

Keywords

33D4533D2033C4530E05q-integralq-orthogonal polynomialsassociated polynomialsq-difference equationsgenerating functionsAl-Salam-Chihara polynomialscontinuous q-ultraspherical polynomials
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 4 , 01 August 2002 , pp. 709 - 735
Copyright
Copyright © Canadian Mathematical Society 2002

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