While investigating the Exton's list of twenty one hyper-geometric functions of four variables and the Sharma's and Parihar's list of eighty three hyper-geometric functions of four variables, we noticed existence of new hyper-geometric series of four variables. The principal object of this paper is to introduce new hyper-geometric series of four variables and present a natural further step toward the mathematical integral presentation concerning these new series of four variables. Integral representations of Euler type and Laplace type involving Appell's hyper-geometric functions and the Horn's series of two variables, Exton's and Lauricella's triple functions and Sharma and Parihar hyper-geometric functions of four variables are established.
Bin-Saad, Maged and Younis, Jihad
Certain Quadruple Hypergeometric Series and their Integral Representations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
2, Article 29.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss2/29