Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0

Abstract

Recently, Kim (2011) has introduced the q-Bernoulli numbers with weight α. In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated with q-Bernoulli numbers and polynomials with weight 0. From these integral representation on ℤp, we derive some interesting identities on the q-Bernoulli numbers and polynomials with weight 0.