Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(6): 1951-1967

Online first article July 7, 2017      Printed November 30, 2017

https://doi.org/10.4134/BKMS.b160560

Copyright © The Korean Mathematical Society.

An extension of the extended Hurwitz-Lerch Zeta Functions of Two Variables

Junesang Choi, Rakesh K. Parmar, Ram K. Saxena

Dongguk University, Government College of Engineering and Technology, Jai Narain Vyas University

Abstract

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

Keywords: Hurwitz-Lerch Zeta function, extended Hurwitz-Lerch Zeta functions, Gauss hypergeometric function, Fox-Wright hypergeometric function, Mellin-Barnes contour integral representations, analytic continuation

MSC numbers: Primary 11M25, 11M99, 33B15, 33C60; Secondary 11M35, 11B68, 33C05, 33C90

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