On Carlitz's trilinear generating functions

In this paper, Carlitz's trilinear generating functions for Rogers-Szegö and Hahn polynomials are obtained by using Carlitz's q-operator. In addition, an equivalent proof of Srivastava-Jain's mixed trilinear generating function is gained. Moreover, a Carlitz's trilinear generating function is deduced. At last, an application to the multiple Carlitz's generating functions for Hahn polynomials is given.