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.
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Funding
The research work of the second-named author (M. P. Chaudhary) was sponsored by the Major Research Project of the National Board of Higher Mathematics (NBHM) of the Department of Atomic Energy (DAE) of the Government of India by its sanction letter (Reference Number 02011/12/2020 NBHM (R. P.)/R D II/7867) dated 19 October 2020. The third-named author (Sangeeta Chaudhary) was sponsored by the UGC-Dr. D. S. Kothari Post-Doctoral Fellowship Scheme under the Grant Number F.4-2/2006 (BSR)/MA/18-19/0022.
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Srivastava, H.M., Chaudhary, M.P., Chaudhary, S. et al. Jacobi’s Triple-Product Identity and an Associated Family of Theta-Function Identities. Math Notes 112, 755–762 (2022). https://doi.org/10.1134/S0001434622110116
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DOI: https://doi.org/10.1134/S0001434622110116