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1. CJM 2002 (vol 54 pp. 709)

Ismail, Mourad E. H.; Stanton, Dennis
$q$-Integral and Moment Representations for $q$-Orthogonal Polynomials
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 $\mathcal{E}_q$.

Keywords:$q$-integral, $q$-orthogonal polynomials, associated polynomials, $q$-difference equations, generating functions, Al-Salam-Chihara polynomials, continuous $q$-ultraspherical polynomials
Categories:33D45, 33D20, 33C45, 30E05

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