H. M. Srivastava, M. P. Chaudhary, S. Chaudhary, G. A. Salilew, “Jacobi's Triple-Product Identity and an Associated Family of Theta-Function Identities”, Mat. Zametki, 2022, Volume 112, Issue 5,Pages <nobr>755

Papers published in the English version of the journal

Jacobi's Triple-Product Identity and an Associated Family of Theta-Function Identities

H. M. Srivastava^abcd, M. P. Chaudhary^e, S. Chaudhary^f, G. A. Salilew^g

^a Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4 Canada
^b Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402 Taiwan
^c Section of Mathematics, International Telematic University Uninettuno, Rome, I-00186 Italy
^d Department of Mathematics and Informatics, Azerbaijan University, Baku, AZ1007 Azerbaijan
^e Department of Mathematics, Netaji Subhas University of Technology, New Delhi, 110078 India
^f School of Computer and System Sciences, Jawaharlal Nehru University, New Delhi, 110067 India
^g Department of Mathematics, Debark University, Debark, North Gondar Zone, Ethiopia

Abstract: The main object of this paper is to present a family of $q$-series identities which involve some of the theta functions of Jacobi and Ramanujan. Each of these (presumably new) $q$-series identities reveals interesting relationships among three of the theta-type functions which stem from the celebrated Jacobi's triple-product identity in a remarkably simple way. The results presented in this paper are motivated essentially by a number of recent works dealing with the subject matter which is investigated herein.

Keywords: theta-function identities, Jacobi's triple-product identity, Ramanujan's theta functions, $q$-series identities, quadratic forms and elliptic functions, number theory and the theory of partitions.

Received: 01.12.2020
Revised: 22.06.2022

Language: English