An extension of the extended Hurwitz-Lerch Zeta Functions of Two Variables
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 1951-1967
Published online July 7, 2017
Printed November 30, 2017
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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