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

SIGMA 20 (2024), 103, 6 pages      arXiv:2408.00377      https://doi.org/10.3842/SIGMA.2024.103
Contribution to the Special Issue on Basic Hypergeometric Series Associated with Root Systems and Applications in honor of Stephen C. Milne

Rogers-Ramanujan Type Identities Involving Double Sums

Dandan Chen ab and Siyu Yin a
a) Department of Mathematics, Shanghai University, P.R. China
b) Newtouch Center for Mathematics, Shanghai University, P.R. China

Received August 02, 2024, in final form November 13, 2024; Published online November 19, 2024

Abstract
We prove four new Rogers-Ramanujan-type identities for double series. They follow from the classical Rogers-Ramanujan identities using the constant term method and properties of Rogers-Szegő polynomials.

Key words: Rogers-Ramanujan type identities; sum-product identities; constant term method.

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