Some expansion formulas for a class of generalized Hurwitz-Lerch zeta functions. (English) Zbl 1172.11026

Summary: By making use of fractional calculus, the authors present a systematic investigation of expansion and transformation formulas for several general families of the Hurwitz-Lerch zeta-functions. Relevant connections of the results discussed here with those obtained in earlier works are also indicated precisely.


11M35 Hurwitz and Lerch zeta functions
26A33 Fractional derivatives and integrals
33C05 Classical hypergeometric functions, \({}_2F_1\)
11B68 Bernoulli and Euler numbers and polynomials
11B73 Bell and Stirling numbers
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