On a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials

Abstract

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pintér addition theorem is obtained. Some new identities involving $q$-polynomials are proved.