Relations between Rα, Rβ and Rm functions related to Jacobi’s triple-product identity and the family of theta-function identities

In this paper, the author establishes a set of three new theta-function identities involving Rα, Rβ 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 answer a open question of Srivastava et al [33], and established relations in terms of Rα, Rβ and Rm (for m = 1, 2, 3), and q-products identities. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities.