Family of Theta-Function Identities Involving Rα and Rm-Functions Related to Jacobi's Triple-Product Identity.

The authors establish a set of four new theta-function identities involving R_α and Rm-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 R_α and R_m-Functions to several interesting q-identities such as (for example) a number of q-product identities and Jacobi's celebrated triple-product identity. Several recent developments on the subject-matter of this article as well as some of its potential application areas are also briefly indicated. [ABSTRACT FROM AUTHOR]