(q,c)-Derivative operator and its applications

Abstract

In this paper, we introduce new concept of (q,c)-derivative operator of an analytic function, which generalizes the ordinary q-derivative operator. From this definition, we give the concept of (q,c)-Rogers-Szegö polynomials, and obtain the expanded theorem involving (q,c)-Rogers-Szegö polynomials. In addition, we construct two kinds (q,c)-exponential operators, apply them to (q,c)-exponential functions, and establish some new identities. At last, some properties of (q,c)-Rogers-Szegö polynomials are discussed.