Abstract
In this paper, we show how to deduce Askey–Wilson type integrals by the method of q-difference equation. In addition, we construct the relation between bilinear generating functions and solutions of q-difference equation. More over, we generalize Bailey's ψ66 summation from the perspective of q-integral by the method of q-difference equation. At last, we deduce U(n+1) type generating functions for Al-Salam–Carlitz polynomials by the method of q-difference equation.
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