Abstract
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.
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