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Some relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol-type polynomials. (English) Zbl 1347.26021

Summary: 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 Fractional derivatives and integrals
11M35 Hurwitz and Lerch zeta functions
33C05 Classical hypergeometric functions, \({}_2F_1\)
11B68 Bernoulli and Euler numbers and polynomials
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