Notes on Askey–Roy integral and certain generating functions for -polynomials

In this paper, generalizations of Askey–Roy integral are given by the technique of transformation. In addition, a recurring formula for Askey–Roy integral and an integral involving Cauchy polynomial are deduced by Askey–Roy integral. Besides, a new transformation identity is gained by Askey–Roy integral. Moreover, a certain generating function for generalized Al-Salam–Carlitz polynomials is obtained by Askey–Roy integral. At last, two generalizations of U ( n + 1 ) type generating function for generalized Al-Salam–Carlitz polynomials are derived by Askey–Roy integral.