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In this paper, we present three new expansion formulas for the generalized Hurwitz-Lerch zeta function. These expansions are obtained by using Taylor-like expansions involving fractional derivatives. Finally, interesting special cases involving the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials are also given. MSC:26A33, 11M35, 33C05, 11B68.

advances in difference equations

Some relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol-type polynomials