Expand all
Collapse all
|
Results 1 - 1 of 1 |
1. CJM 1997 (vol 49 pp. 520)
|
Classical orthogonal polynomials as moments 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.
Keywords:Classical orthogonal polynomials, \ACP, continuous, $q$-ultraspherical polynomials, generating functions, multilinear, generating functions, transformation formulas, umbral calculus Categories:33D45, 33D20, 33C45, 30E05 |