Q-Difference equations of moment integrals for transformational identities and generating functions

Abstract

In this paper, we show how to deduce several moment integrals by the method of -difference equation. In addition, we obtain several generalizations of transformational identities by the technique of moment integrals. Meanwhile, we obtain some special cases of bilateral–unilateral series and the Rogers–Ramanujan identities as by-products. Moreover, we give two mixed generating functions for generalized Rogers–Szegö polynomials by moment integrals and derive two transformational identities by symmetry. At last, a trilinear generating function for generalized Rogers–Szegö polynomials is given by moment integrals.