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arXiv · 1810.02918

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

Zhi-Guo Liu
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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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Zhi-Guo Liu. 2018-10-06. Askey--Wilson polynomials and a double $q$-series transformation formula with twelve parameters. https://arxiv.org/abs/1810.02918

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