Applications of the Operator T in q-Polynomials

Abstract

In this paper, we define the polynomials . In order to determine the generating function, Rogers’ formula, Mehler’s formula, and their extensions for polynomials , we utilize the -exponential operator . Some results for the Cauchy polynomials  and the bivariate Rogers-Szegö polynomials  are obtained by inserting special values into the identities of the polynomials .