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Mathematica Moravica
2017, vol. 21, iss. 2, pp. 75-84
article language: English
document type: unclassified
published on: 26/01/2018
doi: 10.5937/MatMor1702075A
Creative Commons License 4.0
General integral formulas involving Hubert hypergeometric functions of two variables
aDepartment of Mathematics Faculty of Education-Shabwah Aden University, Aden, Yemen
bDepartment of Mathematics Faculty of Education-Shabwa Aden University, Aden, Yemen

e-mail: ah-a-atash@hotmail.com

Abstract

In this paper, we have established two general integral formulas involving Humbert hypergeometric functions of two variables ψ2 and 2. The results are obtained with the help of a generalization of classical Kummer's summation theorem on the sum of the series 2F1(-1) due to Lavoie et al. [5]. Some interesting applications are also presented.

Keywords

Humbert functions; Exton functions; Kampé de Férietfunction; Integral formulas; Kummer's theorem

References

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Erdélyi, A., Magnus, W., Oberhettinger, F., F.G. (1953) Tricomi, Higher Transcendental Functions, Vol. I. New York, Toronto: McGraw-Hill
Exton, H. (1972) Certain hypergeometric functions of four variables. Bull. Soc. Math. Gréce, (N. S.), 104-113; 13
Exton, H. (1976) Multiple Hypergeometric Functions and Applications. New York: John Wiley and Sons (Halsted Press)
Lavoie, J.L., Grondin, F., Rathie, A.K. (1996) Generalizations of Whipple's theorem on the sum of a 3F2. Journal of Computational and Applied Mathematics, 293-300; 72
Rainville, E.D. (1960) Special Functions. New York: The Macmillan Company
Srivastava, H.M., Karlsson, P.W. (1985) Multiple Gaussian Hypergeometric series. New York: Halsted Press
Srivastava, H.M., Manocha, H.L. (1984) A treatise on generating functions. New York: Halsted Press