” Carlitz type and Bernoulli Identities”

Abstract

By using an explicit formula for Bernoulli polynomials we ob tained in a recent work Bn(y)is written as a linear combination of the(y −r) n ; r = 1, 2, 3, · · · k + 1 where k ≥ n polynomials it is pos sible to obtain Bernoulli polynomial identities from polynomial combinatorics identities. Using this approach, we obtain some generalizations and new demonstrations of the 1971 Carlitz iden tity involving Bernoulli numbers, and we also obtain some new identities involving Bernoulli polynomials.