Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 520-542 |
| Number of pages | 23 |
| Journal | Canadian Journal of Mathematics |
| Volume | 49 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 1997 |
Keywords
- Al-Salam-Chihara polynomials
- Classical orthogonal polynomials
- Continuous q-ultraspherical polynomials
- Generating functions
- Multilinear generating functions
- Transformation formulas
- Umbral calculus