Some remarks on the generalized Apostol-Bernoulli and Apostol-Euler polynomials

Abstract

In this paper, we give explicit expressions for generalized Apostol-Bernoulli and Apostol-Euler polynomials. As consequences, we deduce some explicit representations for other Apostol-type polynomials. Moreover, we find an algorithm based on a three-term recurrence for the calculation of generalized Apostol-Euler numbers and polynomials. As an application, we derive a formula for the values of some kinds of Hurwitz-Lerch Zeta functions at negative arguments.