IDENTITIES OF A GENERAL MULTIPLE HURWITZ-LERCH ZETA FUNCTION AND APPLICATIONS
By
R. C. Singh Chandel1, M. A. Pathan2 and Hemant Kumar3
1Former Head, Department of Mathematics D. V. Postgraduate College Orai, Uttar Pradesh, India-285001
2Centre for Mathematical and Statistical Sciences, Peechi Campus, Peechi, Kerala, India-680653
3Department of Mathematics, Aligarh Muslim University, Aligarh, India-202002
3Department of Mathematics, D. A-V. Postgraduate College Kanpur, Uttar Pradesh, India-208001
Email: rc_chandel@yahoo.com, mapathan@gmail.com, palhemant2007@rediffmail.com
(Received: August 04, 2023; In format: September 03, 2023; Accepted: September 12, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53211
Abstract
In this article we introduce a general multiple Hurwitz-Lerch Zeta function. Then its convergence conditions and identities are obtained under certain conditions. We also derive some of connections to the multiple Hurwitz-Lerch Zeta function based upon Srivastava-Daoust hypergeometric series in several variables and other related functions of one and more variables found in the literature. Further, we study its integral representations and nd their applications for deriving generating relations and solving the non-homogeneous fractional differential equation.
2020 Mathematical Sciences Classification: 11M35, 33C65, 33C70.
Keywords: General multiple Srivastava-Daoust-Hurwitz-Lerch Zeta function, Convergence conditions, Identities, Integral representations, Fractional differential equation.