We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].
The structure relation for Askey-Wilson polynomials
Symmetry of terminating series representations of the Askey-Wilson polynomials
Automorphisms of the DAHA of type $\check{C_1}C_1$ and their action on Askey-Wilson polynomials and functions. I. The flip $(a,b,c,d)\mapsto(a,b,qd^{-1},qc^{-1})$
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