Classical Orthogonal Polynomials as Moments

Ismail, Mourad E. H. ; Stanton, Dennis

Canadian journal of mathematics, Tome 49 (1997) no. 3, pp. 520-542

Résumé

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.

Détail

DOI : 10.4153/CJM-1997-024-9

Mots-clés : 33D45, 33D20, 33C45, 30E05, Classical orthogonal polynomials, Al-Salam-Chihara polynomials, continuous q-ultraspherical polynomials, generating functions, multilinear generating functions, transformation formulas, umbral calculus

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