Rogers-Ramanujan Type Identities Involving Double Sums

TL;DR

This paper introduces four new Rogers-Ramanujan-type identities involving double sums, derived from classical identities using the constant term method and properties of Rogers-Szegő polynomials.

Contribution

It presents novel identities of Rogers-Ramanujan type involving double series, expanding the mathematical understanding of these identities through new proof techniques.

Findings

Four new Rogers-Ramanujan-type identities for double series

Identities derived using constant term method and Rogers-Szegő polynomials

Enhances the theoretical framework of q-series and partition identities

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-Szeg\H{o} polynomials.