A Study of Generalized Hurwitz-Lerch Zeta Function of Two-variables and Threevariables and its terms of Extended Beta Function
Main Article Content
Abstract
The main aim of this paper is to introduce a new extension of the generalized Hurwitz-Lerch Zeta functions of two variables [abbreviated as H-L-Z-F-2V] and three variables [abbreviated as H-L-Z-F-3V] involving the extended Beta function. We then systematically investigate its several interesting properties and related formulas as (for example) various integral representations, which provide certain new and known extensions of earlier corresponding results, a derivative formula, and Mellin-transform. We also consider some important special cases.
Downloads
Article Details
Section
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
References
J. Choi, D. S. Jang, H. M. Srivastava; A generalization of the Hurwitz–Lerch zeta function, Integral Transforms Spec. Funct., 19 (2008), 65-79.
M. Garg, K, Jain, S. L. Kalla; A further study of general Hurwitz–Lerch zeta function, Algebras Groups Geom., 25 (2008), 311-319.
R. Nadeem, T. Usman, K. S. Nisar, D. Baleanue; Analytical properties of the Hurwitz-Lerch Zeta function, Advances in Difference Equations, 466 (2020).
R. K. Parmar, R. K. Raina; On a certain extension of the Hurwitz–Lerch zeta function, An. Univ. Vest. Timi¸s., Ser. Mat.-Inform., 2 (2014), 157-170.
H. M. Srivastava, J. Choi; Series Associated with the Zeta and Related Functions, Kluwer Acedemic, Dordrecht, 2001.
H. M. Srivastava; Generating relations and other results associated with some families of the extended Hurwitz–Lerch zeta functions, SpringerPlus, 2013.
H. M. Srivastava, M. J. Luo, R. K. Raina; New results involving a class of generalized Hurwitz–Lerch zeta functions and their applications, Turk. J. Anal. Number Theory 1-1 (2013), 26-35.
G. Rahman, K. S. Nisar, M. Arshad; A new extension of Hurwitz–Lerch Zeta function, arXiv:1802.07823 (2018).
G. Rahman, K. S. Nisar, S. A. Mubeen; (p,v)-extension of Hurwitz–Lerch Zeta function and its properties. Preprints, (2018) https://doi.org/10.20944/preprints201803.0008.v1.
E. D. Rainville; Special Functions; The Macmillan Company: New York, USA, 1960.
R. K. Raina, P. K. Chhajed; Certain results involving a class of functions associated with the Hurwitz zeta function, Acta Math. Univ. Comen., 73 (2004), 89-100.
J. Choi, A. K. Rathie, R. K. Parmar; Extension of extended beta, hypergeometric and confluent hypergeometric functions, Honam Math. J., 36-2 (2014), 357-385.
M. A. Pathan, O. Daman; Further generalizations of Hurwitz-Lerch Zeta function, Math. Sci. Res. J., 16 (2012), 251-259.
J. Choi, R. K. Parmar; An extension of the generalized Hurwitz-Lerch Zeta function of two variable, Filomat, 31 (2017), 91-96.
K. S. Nisar; Further extension of the generalized Hurwitz–Lerch zeta function of two variables, Mathematics, 48-7 (2019).
H. M. Srivastava, P. W. Karlsson; Multiple Gaussian Hypergeometric Series, Halsted, New York, 1985.
H. M. Srivastava, J. Choi; Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, Amsterdam, 2012.
S. D. Lin, H. M. Srivastava; Some families of the Hurwitz–Lerch zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput., 154 (2004), 725-733.