Askey–Wilson polynomials and a double 𝑞-series transformation formula with twelve parameters

Liu, Zhi-Guo

doi:10.1090/proc/14411

Askey–Wilson polynomials and a double $q$-series transformation formula with twelve parameters
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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 $_2F_1$ 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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