Dedekind's eta-function and Rogers-Ramanujan identities

TL;DR

This paper proves a new q-series identity that extends classical eta-function and Rogers-Ramanujan identities, with conjectures for further generalizations including Andrews-Gordon identities.

Contribution

It introduces a generalized q-series identity that unifies and extends key identities in the theory of partitions and modular forms.

Findings

Proved a generalized eta-function identity.

Extended Rogers-Ramanujan identities.

Conjectured further generalizations including Andrews-Gordon identities.

Abstract

We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)} eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities.