Askey--Wilson polynomials and a double q-series transformation formula with twelve parameters
Abstract
The Askey--Wilson polynomials are the most general classical orthogonal polynomials that are known and the Nassrallah--Rahman integral is a very general extension of Euler's integral representation of the classical 2F1 function. Based on a q-series transformation formula and the Nassrallah--Rahman integral we prove a q--beta integral which has twelve parameters, with several other results, both classical and new, included as special cases. This q-beta integral also allows us to derive a curious double q--series transformation formula, which includes one formula of Al--Salam and Ismail as a special case
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