Abstract
The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 501-520 |
| Number of pages | 20 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 421 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2015 |
Bibliographical note
Publisher Copyright:© 2014 Elsevier Inc.
Keywords
- Askey-Wilson polynomials
- Hermite polynomials
- Moments
- Orthogonal polynomials