# The Incomplete Lauricella Functions of Several Variables and Associated Properties and Formulas

• Choi, Junesang (Department of Mathematics, Dongguk University) ;
• Parmar, Rakesh K. (Department of Mathematics, Government College of Engineering and Technology) ;
• Srivastava, H.M. (Department of Mathematics and Statistics, University of Victoria)
• Accepted : 2016.12.06
• Published : 2018.03.23

#### Abstract

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

#### Acknowledgement

Supported by : Dongguk University, Natural Sciences and Engineering Research Council of Canada

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