On a symmetric $q$-series identity

TL;DR

This paper proves a symmetric $q$-series identity that generalizes Ramanujan's result, providing both an analytic proof and a bijective-type proof outline.

Contribution

It introduces a new symmetric $q$-series identity extending Ramanujan's work, with dual proof methods.

Findings

The identity generalizes Ramanujan's original result.

Analytic proof confirms the identity rigorously.

Bijective-type proof outline offers combinatorial insight.

Abstract

We prove an interesting symmetric $q$-series identity which generalizes a result due to Ramanujan. A proof that is analytic in nature is offered, and a bijective-type proof is also outlined.