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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[1] Srivastava H. M., Series Associated with the Zeta and Related Functions (2001) · Zbl 1014.33001
[2] Yen C.-E., Journal of Fractional Calculus 22 pp 99– (2002)
[3] Nishimoto K., Journal of Fractional Calculus 22 pp 91– (2002) · Zbl 1033.26010
[4] DOI: 10.1016/S0096-3003(03)00746-X · Zbl 1078.11054
[5] Goyal S. P., Ganita Sandesh 11 pp 99– (1997)
[6] Erdélyi A., Higher Transcendental Functions 1 (1953) · Zbl 0051.30303
[7] DOI: 10.1017/S0305004100004412 · Zbl 0978.11004
[8] Whittaker E. T., A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, 4. ed. (1927) · JFM 53.0180.04
[9] Garg M., Integral Transforms and Special Functions
[10] Erdélyi A., Tables of Integral Transforms 2 (1954) · Zbl 0055.36401
[11] Podlubny I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications 198 (1999) · Zbl 0924.34008
[12] Miller K. S., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993) · Zbl 0789.26002
[13] DOI: 10.1017/S1446181100008154 · Zbl 1052.33005
[14] Nörlund N. E., Vorlesungen über Differentzenrechnung (1924)
[15] Luke Y. L., The Special Functions and Their Approximations, Vol. 1 53 (1969) · Zbl 0193.01701
[16] DOI: 10.1016/S0893-9659(04)90077-8 · Zbl 1070.33012
[17] DOI: 10.1016/0022-247X(88)90326-5 · Zbl 0621.33008
[18] Kilbas A. A., Theory and Applications of Fractional Differential Equations 204 (2006) · Zbl 1138.26300
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