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Maged G. Bin-Saad, Department of Mathematics, Aden University, Aden, Kohrmaksar , P.O.Box 6014,Yemen
Amani M. Hanballa, Department of Mathematics, Aden University, Aden, Kohrmaksar , P.O.Box 6014,Yemen
In this work we will introduce and study a generalized zeta function of the general Hurwitz – Lerch zeta functions. Here, we aim to derive basic properties of generalized zeta function for the general Hurwitz – Lerch zeta functions include some integral representations for several general Hurwitz – Lerch zeta functions and fractional derivative. A number of known and new results which introduced are generalization of a known results introduced by Shy-Der and Srivastava .
Hurwitz-Lerch zeta functions; Mellin-Barnes integrals; hypergeometric functions; hypergeomteric-type generating functions.
Cite this paper
Maged G. Bin-Saad, Amani M. Hanballa, ON HYPERGEOMETRIC SERIES ASSOCIATED WITH THE GENERALIZED ZETA FUNCTIONS, SCIREA Journal of Mathematics. Vol. 1 , No. 1 , 2016 , pp. 53 - 62 .
|[ 1 ]||Erdélyi, A., Magnw,W., Oberhettinger, F. and Tricomi, F.G.,Higher Transcendental Functions, Vol.I , McGraw – Hill book inc. New York, Toronto and London, 1953.|
|[ 2 ]||Erdélyi, A., Magnw,W., Oberhettinger, F. and Tricomi, F.G., Tables of Integral Transforms, Vol.2 , McGraw – Hill book inc. New York, Toronto and London, 1954.|
|[ 3 ]||Goyal, S, P. and Laddha, R. K., On the generalized Riemann zeta functions and the generalized Lambert transform, Gahnite Sandesh, Vol.2 Dec.(1997), 99-108.|
|[ 4 ]||Miller, K.S.and Rose, B., An introduction to The Fractional Calculus and Fractional Differential Equations, New York, 1993.|
|[ 5 ]||Srivastava, H. M., and Choi, J., Series associated with the zeta and Related function, Kluwee Academic Publishers, Dordrecht,2001|
|[ 6 ]||Shy-Der Lin, Srivastava, H. M., Some families of the Hurwitz-Lerch zeta functions and associated fractional derivative and other integral representations, Applied Mathematics and Computation 154(2004) 725-733.|
|[ 7 ]||Srivastava, H. M. and Karlsson, P. W., Multiple Gaussian Hypergeometric Series, Halsted Press, Brisbane, New York and Toronto 1985.|