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Appell functions

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Full-Text Articles in Special Functions

Certain Quadruple Hypergeometric Series And Their Integral Representations, Maged Bin-Saad, Jihad Younis Dec 2019

Certain Quadruple Hypergeometric Series And Their Integral Representations, Maged Bin-Saad, Jihad Younis

Applications and Applied Mathematics: An International Journal (AAM)

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 …


Extension Formulas Of Lauricella’S Functions By Applications Of Dixon’S Summation Theorem, Ahmed A. Atash Dec 2015

Extension Formulas Of Lauricella’S Functions By Applications Of Dixon’S Summation Theorem, Ahmed A. Atash

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this research paper is to obtain two extension formulas for the first and second kind of Lauricella’s functions of three variables with the help of generalized Dixon’s summation theorem, which was obtained by Lavoie et al. In addition to this, two extension formulas for the second and third kind of Appell’s functions are obtained as a consequence of the above mentioned results . Furthermore, some transformation formulas involving Exton’s double hypergeometric series are obtained as an applications of our main results.