q-integral and moment representations for q-orthogonal polynomials

Mourad E.H. Ismail; Dennis Stanton

doi:10.4153/CJM-2002-027-2

q-integral and moment representations for q-orthogonal polynomials

Mourad E.H. Ismail, Dennis Stanton

Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

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 ε_q.

Original language	English (US)
Pages (from-to)	709-735
Number of pages	27
Journal	Canadian Journal of Mathematics
Volume	54
Issue number	4
DOIs	https://doi.org/10.4153/CJM-2002-027-2
State	Published - Aug 2002

Keywords

Al-Salam-Chihara polynomials
Associated polynomials
Continuous q-ultraspherical polynomials
Generating functions
q-difference equations
q-integral
q-orthogonal polynomials

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KW - Generating functions

KW - q-difference equations

KW - q-integral

KW - q-orthogonal polynomials

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q-integral and moment representations for q-orthogonal polynomials

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Keywords

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