A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity
Open Access
- 5 June 2020
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 8 (6), 918
- https://doi.org/10.3390/math8060918
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
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