Volume 1, Number 1 (2016)
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Home > Journals > SCIREA Journal of Mathematics > Archive > Paper Information

ON HYPERGEOMETRIC SERIES ASSOCIATED WITH THE GENERALIZED ZETA FUNCTIONS

Volume 1, Issue 1, October 2016    |    PP. 53-62    |PDF (485 K)|    Pub. Date: October 19, 2016
2284 Downloads     12822 Views  

Author(s)
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

Abstract
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 [6].

Keywords
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 .

References

[ 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.

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