Srivastava, H.M.Srivastava, RekhaChaudhary, Mahendra PalUddin, Salah2020-07-102020-07-1020202020Srivastava, H. M., Srivastava, R., Chaudhary, M. P., & Uddin, S. (2020). A family of theta-function identities based upon combinatorial partition identities related to Jacobi’s triple-product identity. Mathematics, 8(6). https://doi.org/10.3390/math8060918https://doi.org/10.3390/math8060918http://hdl.handle.net/1828/11921The 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.entheta-function identitiesmultivariable R-functionsJacobi's triple-product identityRamanujan's theta functionsq-product identitiesEuler's pentagonal number theoremRogers-Ramanujan continued fractionRogers-Ramanujan identitiescombinatorial partition-theoreticSchur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identitiesSchur’s second partition theoremArticle