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Lin, Shy-Der; Srivastava, H. M.; Wang, Pin-Yu

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

Integral Transforms Spec. Funct. 17, No. 11, 817-827 (2006).
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.

Cited in 1 Review
Cited in 48 Documents

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

Keywords:

fractional calculus; expansion formulas; Lerch’s functional equation; Lerch’s transformation formula; Hurwitz-Lerch zeta functions; Lipschitz-Lerch zeta functions; Riemann-Liouville fractional derivative; Leibniz rule; Hurwitz zeta function; generalized zeta function; Riemann zeta function; sum-integral representations; Bernoulli polynomials and Bernoulli numbers of higher order; Fox-Wright generalized hypergeometric function; Eulerian integral of the first kind
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\textit{S.-D. Lin} et al., Integral Transforms Spec. Funct. 17, No. 11, 817--827 (2006; Zbl 1172.11026)
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