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An extension of the generalized Hurwitz-Lerch Zeta function of two variables

Choi Junesang (Dongguk University, Department of Mathematics, Gyeongju, Republic of Korea)
Parmar Rakesh K. (Government College of Engineering and Technology, Department of Mathematics, Bikaner, Rajasthan State, India)

The main object of this paper is to introduce a new extension of the generalized Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate such its several interesting properties and related formulas as (for example) various integral representations, which provide certain new and known extensions of earlier corresponding results, a summation formula and Mellin-Barnes type contour integral representations. We also consider some important special cases.

Keywords: Gamma function, Beta function, Hypergeometric function, Generalized Hurwitz-Lerch Zeta function, Gauss’s Hypergeometric function, Appell hypergeometric function, Mellin-Barnes contour integral, Summation formula