Identities of symmetry for generalized Bernoulli polynomials

Abstract

In this paper, we derive eight basic identities of symmetry in three variables related to generalized Bernoulli polynomials and generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the $p$-adic integral expression of the generating function for the generalized Bernoulli polynomials and the quotient of $p$-adic integrals that can be expressed as the exponential generating function for the generalized power sums.