Generating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions
Date
2013-02-25
Authors
Srivastava, H.M.
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Volume Title
Publisher
SpringerPlus
Abstract
Motivated essentially by recent works by several authors (see, for example, Bin-Saad [Math J Okayama Univ 49:37–52, 2007] and Katsurada [Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13–25, 1997], the main objective in this paper is to present a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associated with various classes of the extended Hurwitz-Lerch Zeta functions. Our main results would generalize and extend the aforementioned recent work by Bin-Saad [Math J Okayama Univ 49:37–52, 2007] (see also Katsurada [Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13–25, 1997]). We also show the hitherto unnoticed fact that the so-called τ-generalized Riemann Zeta function, which happens to be the main subject of investigation by Gupta and Kumari [Jñānābha 41:63–68, 2011]) and Saxena et al. [J Indian Acad Math 33:309–320, 2011], is simply a seemingly trivial notational variation of the familiar general Hurwitz-Lerch Zeta function Φ(z,s,a). Finally, we present a sum-integral representation formula for the general family of the extended Hurwitz-Lerch Zeta functions.
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SpringerOpen
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Citation
Srivastava, H. (2013). Generating relations and other results associated with some families of the extended hurwitz-lerch zeta functions. Springerplus, 2(1), 67.