Certain Identities of a General Class of Hurwitz-Lerch Zeta Function of Two Variables

Abstract

In this paper, we introduce a generalized double Hurwitz-Lerch Zeta function and then systematically investigate its properties and various integral representations. Further, we show that these results provide certain known as well as new extensions of earlier stated results of generalized Hurwitz-Lerch Zeta functions.

On Arithmetic Functions, Their Extended Coefficients: Various Results and Relations

“…In this section we introduce some extensions of the arithmetic function (1.1) and the identity (3.5). Then make their applications to derive some more other results connected to Bell polynomials [16,17,18] and the Riemann Zeta functions [13,19,24]. For the g j ∀j ≥ 1, given in (1.5), one of the extensions of (1.1) is taken by…”

“…Then make an appeal to the formula (4.3) of the Theorem 4.1 to find the function (4.7). For the generalized Riemann Zeta function defined and studied by[13,19,24] a) s , ∀a.s ∈ C and (a) > 0, (s) > 1, and…”

Identities of a General Multiple Hurwitz-Lerch Zeta Function and Applications

“…Here in this research article, in order to explore new ideas for studying various known and unknown Hurwitz-Lerch Zeta functions of one, two and multiple Hurwitz-Lerch Zeta functions (see in [5,6,7,8,10,11,13,14,15,16,17,19]), we introduce a general multiple Hurwitz-Lerch Zeta function given by (1.10)…”

“…along with η, c∈ C\Z 0 .4 Integral representations of the multiple Hurwitz-Lerch Zeta function (1.10)We use the Eulerian integral formula[8,10,11] and find an integral representation of the multiple Hurwitz-…”

Relations and Identities Due to Double Series Associated With General Hurwitz-Lerch Type Zeta Functions

“…But when z = 1, we apply the techniques of Gaussian gamma function ( [6], [7], [12]) and then Watson's theorem (see [14,p.54,Eqn. (2.3.3.13)], [18,p.…”