On Oliver's relations between infinite series and infinite products

The Jacobi triple product identity provides closed-form expressions for many infinite-product generating functions that arise naturally in combinatorics and number theory.

A particularly important application is to Dedekind's eta function {\eta}({\tau}), which it expresses as a theta function.

Using the theory of modular forms, Oliver [5] classified all eta quotients that are theta functions.

In this paper, we present elementary proofs of the identities established by Oliver.