A note on generating functions for Rogers-Szego polynomials

Abstract

In this paper, the details of certain Carlitz's generating functions for Rogers-Szego polynomials and their generalizations are given by Carlitz's q-operators. In addition, an additional proof of Srivastava-Jain's generating function is shown. At last, generalizations of Srivastava-Agarwal type generating functions are obtained.

Keywords: Rogers-Szego polynomials, generating function, Al-Salam-Carlitz polynomials, Carlitz's q-operators, Srivastava-Agarwal type generating functions

Quaestiones Mathematicae 35(2012), 447-461