A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

Hari Mohan Srivastava, Rekha Srivastava, Mahendra Pal Chaudhary and Salah Uddin
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Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Rekha Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Mahendra Pal Chaudhary: Department of Mathematics, Netaji Subhas University of Technology, Sector 3, Dwarka, New Delhi 110078, India
Salah Uddin: Department of Mathematics, PDM University, Bahadurgarh 124507, Haryana State, India

Mathematics, 2020, vol. 8, issue 6, 1-14

Abstract: The authors establish a set of six new theta-function identities involving multivariable R -functions which are based upon a number of q -product identities and Jacobi’s celebrated triple-product identity. These theta-function identities depict the inter-relationships that exist among theta-function identities and combinatorial partition-theoretic identities. Here, in this paper, we consider and relate the multivariable R -functions to several interesting q -identities such as (for example) a number of q -product identities and Jacobi’s celebrated triple-product identity. Various recent developments on the subject-matter of this article as well as some of its potential application areas are also briefly indicated. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities and present a presumably open problem.

Keywords: theta-function identities; multivariable R -functions; Jacobi’s triple-product identity; Ramanujan’s theta functions; q -product identities; Euler’s pentagonal number theorem; Rogers-Ramanujan continued fraction; Rogers-Ramanujan identities; combinatorial partition-theoretic identities; Schur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identities; Schur’s second partition theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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