New proofs of generating functions for Rogers-Szegö polynomials

In this paper, we show how to use the q-exponential operator to prove four generating functions for Rogers-Szegö polynomials of [L. Carlitz, Generating functions for certain q-orthogonal polynomials, Collectanea Math. 23 (1972), 91-104]. In addition, four auxiliary ones under the replacement q→q-1 are derived by this method.