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Classical Orthogonal Polynomials as Moments

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, 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 show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials.

Keywords

33D4533D2033C4530E05Classical orthogonal polynomialsAl-Salam-Chihara polynomialscontinuous q-ultraspherical polynomialsgenerating functionsmultilinear generating functionstransformation formulasumbral calculus
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 3 , 01 June 1997 , pp. 520 - 542
Copyright
Copyright © Canadian Mathematical Society 1997

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