CERTAIN RESULTS OF GENERALIZED BARNES TYPE DOUBLE SERIES RELATED TO THE HURWITZ-LERCH ZETA FUNCTIONS OF TWO VARIABLES
By
Hemant Kumar
Department of Mathematics, D. A-V. Postgraduate College Kanpur-208001, Uttar Pradesh, India
Email: palhemant2007@rediffmail.com
(Received: July 28, 2022; In format: August 08, 2022; Revised: November 11, 2022; Accepted: November 15, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52222
Abstract
In these researches we introduce a generalized Barnes type double series and then, discuss its convergent conditions. We obtain some of its results related to the known and new Hurwitz -Lerch zeta function of two variables and also derive Eulerian and Mellin- Barnes type integral representations of these functions and analyze various properties these functions.
2020 Mathematical Sciences Classification: Primary 11M35, 33C65, 33E05; Secondary, 33C05, 33C20, 33C60, 33C90.
Keywords and Phrases: Weierstrass elliptic function, Barnes type double series, Hurwitz -Lerch zeta function of two variables, Eulerian and Mellin-Barnes type integrals and special functions.