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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.

MSC:

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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References:

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