Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 059, 10 pages      arXiv:2212.02355      https://doi.org/10.3842/SIGMA.2024.059
Contribution to the Special Issue on Basic Hypergeometric Series Associated with Root Systems and Applications in honor of Stephen C. Milne

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

Hjalmar Rosengren
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg, Sweden

Received March 25, 2024, in final form June 27, 2024; Published online July 02, 2024

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.

Key words: Rogers-Ramanujan identities; constant term identities.

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