Abstract
We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 664-674 |
| Number of pages | 11 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 424 |
| Issue number | 1 |
| DOIs | |
| State | Published - Apr 1 2015 |
Bibliographical note
Publisher Copyright:© 2014 Elsevier Inc.
Keywords
- Andrews formula
- Askey-Wilson polynomials
- Basic hypergeometric series
- Expansion formulas
- Generating functions