q-Integral and Moment Representations for q-Orthogonal Polynomials

Ismail, Mourad E. H. ; Stanton, Dennis

Canadian journal of mathematics, Tome 54 (2002) no. 4, pp. 709-735

Résumé

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 $\text{ }{{\varepsilon }_{q}}$ .

Détail

DOI : 10.4153/CJM-2002-027-2

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

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