A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

Abstract

Abstract. In this paper, we define a (p, v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

Analytical properties of the Hurwitz–Lerch zeta function

“…A more detailed exposition of the various generalizations, properties, and applications of the Hurwitz-Lerch zeta functions could be found in the literature (see [3][4][5][6][7][8][9][10][11][12]). For example Goyal and Laddha [9], Lin and Srivastava [13] and Garg et al [7] established certain remarkable extensions of the Hurwitz-Lerch zeta function Φ δ,ς ;γ (ξ , s, υ) given in Eq.…”