An explicit formula for the generalized Bernoulli polynomials

Abstract The object of the present note is to prove a new explicit formula for the generalized Bernoulli polynomials. The main result (3) below provides an interesting extension of a representation for the generalized Bernoulli numbers given recently by P. G. Todorov [C.R. Acad. Sci. Paris Ser. I Math.301 (1985), 665–666].