Abstract
Previously, we proved a q-series expansion formula which allows us to recover many important classical results for q-series. Based on this formula, we derive a new q-formula in this paper, which clearly includes infinitely many q-identities. This new formula is used to give a new proof of the orthogonality relation for the Askey-Wilson polynomials. A curious q-transformation formula is proved, and many applications of this transformation to Hecke type series are given. Some Lambert series identities are also derived.
| Original language | English |
|---|---|
| Pages (from-to) | 193-210 |
| Number of pages | 18 |
| Journal | Ramanujan Journal |
| Volume | 30 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 2013 |
Keywords
- Askey-Wilson polynomials
- Hecke type series
- Lambert series
- Mock theta functions
- q-series