CLASSICAL ORTHOGONAL POLYNOMIALS AS MOMENTS

Authors
ISMAIL MEH STANTON D
Citation
Meh. Ismail et D. Stanton, CLASSICAL ORTHOGONAL POLYNOMIALS AS MOMENTS, Canadian journal of mathematics, 49(3), 1997, pp. 520-542
Citations number
31
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Canadian journal of mathematics → ACNP
ISSN journal
0008414X
Volume
49
Issue
3
Year of publication
1997
Pages
520 - 542
Database
ISI
SICI code
0008-414X(1997)49:3<520:COPAM>2.0.ZU;2-#
Abstract
We show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in cer tain normalization, are moments of probability measures. We use this f act to derive bilinear rind multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas fo r the Charlier, Hermite and Laguerre polynomials.