Abstract
We prove a general expansion formula in Askey–Wilson polynomials using Bailey transform and Bressoud inversion. As applications, we give new proofs and generalizations of some recent results of Ismail–Stanton and Liu. Moreover, we prove a new q-beta integral formula involving Askey–Wilson polynomials, which includes the Nassrallah–Rahman integral as a special case. We also give a bootstrapping proof of Ismail–Stanton's recent generating function of Askey–Wilson polynomials.
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