Abstract
Using the q-integral representation of Sears' nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us to prove a general q-beta integral formula including the Askey-Wilson integral formula as a special case. Using this double q-integral formula and the theory of q-partial differential equations, we derive a general q-beta integral formula, which includes the Nassrallah-Rahman integral as a special case. Our evaluation does not require the orthogonality relation for the q-Hermite polynomials and the Askey-Wilson integral formula.
| Original language | English |
|---|---|
| Article number | 44 |
| Journal | Symmetry |
| Volume | 8 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2016 |
Keywords
- Double q-integral
- Q-beta integral
- Q-partial differential equation
- Q-series