A New (But Very Nearly Old) Proof of the Rogers-Ramanujan Identities

TL;DR

This paper offers a novel proof of the Rogers-Ramanujan identities utilizing ingredients from Rogers' 1894 work, simplifying the proof process while relying on historically available methods.

Contribution

It provides a new, simpler proof of the Rogers-Ramanujan identities based entirely on tools from Rogers' original 1894 paper, revealing overlooked connections.

Findings

The proof is simpler than previous ones.

All ingredients are from Rogers' 1894 paper.

The identities are confirmed through this new approach.

Abstract

We present a new proof of the Rogers-Ramanujan identities. Surprisingly, all its ingredients are available already in Rogers seminal paper from 1894, where he gave a considerably more complicated proof.