How to Discover the Rogers--Ramunujan Identities

TL;DR

This paper explores a method to conjecture and verify the Rogers-Ramanujan identities, highlighting their historical significance and providing insights into their discovery process.

Contribution

It introduces a novel approach to conjecturing famous identities, demonstrating its effectiveness on the Rogers-Ramanujan identities.

Findings

The method successfully conjectures the Rogers-Ramanujan identities.

The approach offers a new perspective on discovering classical mathematical identities.

It bridges historical conjectures with modern verification techniques.

Abstract

We examine a method to conjecture two very famous identities that were conjectured by Ramanujan, and later found to be known to Rogers.