On Generating Functions of Quadruple Hypergeometric Function

Maged G. Bin-Saad^1, and Jihad Ahmed Younis¹

¹Department of Mathematics, Aden University, Aden, Khormaksar, P.O.Box 6014, Yemen

Cite this paper:
Maged G. Bin-Saad and Jihad Ahmed Younis. On Generating Functions of Quadruple Hypergeometric Function . Turkish Journal of Analysis and Number Theory. 2019; 7(1):5-10. doi: 10.12691/tjant-7-1-2

Abstract

In this work, by using Laplace integral representation of quadruple function defined in [1], we introduce new generating functions involving some triple hyper-geometric functions and itself. Some particular cases and consequences of our main results are also considered.

Keywords:
Laplace transforms triple hyper-geometric functions quadruple hypergeometric functions generating functions

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Maged G. Bin-Saad, A.Younis, Jihad, and R. Aktaş, Integral representations for certain quadruple hyper-geometric series", Far East J. Math. Sci., 103, 21-44.2018.
[2]	Maged G. Bin-Saad and A.Younis, Jihad, "Some Integral Representations for Certain Quadruple Hyper-geometric Functions", MATLAB J., 1, 61-68. 2018.
[3]	H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Lt1., Chichester, 1984.
[4]	P. Agarwal and C. L. Koul, "On generating functions", J. Rajasthan Acad. Phy., Sci. 2(3), 173-180. 2003.
[5]	J. Choi and P. Agarwal, "Certain generating functions involving Appell series", Far East J. Math. Sci., 84, 25-32.2014.
[6]	H. M. Srivastava, "Certain generating functions of several variables", Z. Angew. Math. Mech. 57, 339-340. 1977.
[7]	H. M. Srivastava, P. Agarwal and S. Jain, "Generating functions for the generalized Gauss hyper-geometric functions", Appl. Math. Comput., 247, 348-352.2014.
[8]	H. Exton, "Hyper-geometric functions of three variables", J. Indian Acad. Math. 4, 113-119. 1982.
[9]	Lauricella, G., "Sull funzioni ipergeometric a più variabili.:, Rend. Cric. Mat. Palermo 7, 111-158. 1893.
[10]	A. Erdélyi, W. Magnus, F. Oberhettinger and F. G., Tricomi, Higher Transcendental Functions. Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
[11]	E. D. Rainville, Special Functions, Macmillan Company, New York, 1960, Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
[12]	H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press, Bristone, London, New York and Toronto, 1985.