The Actions on the Generating Functions for the Family of the Generalized Bernoulli Polynomials

Abstract

In this paper, we study the generalization Bernoulli numbers and polynomials
attached to a periodic group homomorphism from a finite cyclic group to the
set of complex numbers and derive new periodic group homomorphism by using a
fixed periodic group homomorphism. Hence, we obtain not only multiplication
formulas, but also some new identities for the generalized Bernoulli
polynomials attached to a periodic group homomorphism.