Some Relationships between the Generalized Apostol-Bernoulli and Apostol-Euler Polynomials

The main objective of this paper is to introduce and investigate two new classes of generalized Apostol-Bernoulli polynomials Bn[m-1,α](x;c,α;λ) and Apostol-Euler polynomials εn[m-1,α](x;c,α;λ). In particular, we obtain addition formula for the new class of the generalized Apostol-Bernoulli polynomials. We also give some recurrence relations and Raabe relations for these polynomials.