A note on moment integrals and some applications

In this paper, two moment integrals are given by the method of transformation. In addition, generalizations of Searsʼs transformation are obtained by moment integrals. Moreover, certain q-Mehler formulas for Rogers–Szegö polynomials are gained by moment integrals. Besides, an open problem of trilinear generating function is deduced by moment integrals. At last, generalizations of U ( n + 1 ) type Kalnins–Miller transformation are achieved by moment integrals.