## 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:

 [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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