Lin, Shy-Der; Srivastava, H. M. Some families of the Hurwitz-Lerch zeta functions and associated fractional derivative and other integral representations. (English) Zbl 1078.11054 Appl. Math. Comput. 154, No. 3, 725-733 (2004). Summary: The main object of this paper is to present, in a unified manner, a number of fractional derivative and other integral representations for several general families of the Hurwitz-Lerch Zeta functions. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely. Cited in 2 ReviewsCited in 64 Documents MSC: 11M35 Hurwitz and Lerch zeta functions 26A33 Fractional derivatives and integrals × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F. G., Higher Transcendental Functions, Vol. I (1953), McGraw-Hill Book Company: McGraw-Hill Book Company New York · Zbl 0052.29502 [2] Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F. G., Tables of Integral Transforms, Vol. II (1954), McGraw-Hill Book Company: McGraw-Hill Book Company New York · Zbl 0055.36401 [3] Goyal, S. P.; Laddha, R. K., On the generalized Riemann Zeta functions and the generalized Lambert transform, \(Ga ṅ\) ita Sandesh, 11, 99-108 (1997) · Zbl 1186.11056 [4] Nishimoto, K.; Yen, C.-E; Lin, M.-L., Some integral forms for a generalized Zeta function, J. Fract. Calc., 22, 91-97 (2002) · Zbl 1018.11043 [5] Podlubny, I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Mathematics in Science and Engineering, Vol. 198 (1999), Academic Press: Academic Press New York · Zbl 0924.34008 [6] Srivastava, H. M.; Choi, J., Series Associated with the Zeta and Related Functions (2001), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 1014.33001 [7] Srivastava, H. M.; Pathan, M. A.; Bin-Saad, M. G., A certain class of generating functions involving bilateral series, ANZIAM J., 44, 475-483 (2003) · Zbl 1052.33005 [8] Whittaker, E. T.; Watson, G. N., 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 (1927), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0951.30002 [9] Yen, C.-E; Lin, M.-L.; Nishimoto, K., An integral form for a generalized Zeta function, J. Fract. Calc., 22, 99-102 (2002) · Zbl 1018.11044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.