Rogers-Ramanujan type identities involving double, triple and quadruple sums

TL;DR

This paper presents new Rogers-Ramanujan type identities involving multiple sums, proven by reduction to known identities using computational and analytical methods, and also derives new single-sum identities as corollaries.

Contribution

It introduces several novel multi-sum Rogers-Ramanujan identities and demonstrates proof techniques that connect them to existing identities, expanding the mathematical understanding of q-series.

Findings

New double, triple, and quadruple sum identities discovered.

Proofs reduce complex sums to known identities via summation and constant term methods.

Additional single-sum identities derived as consequences.

Abstract

We prove a number of new Rogers-Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the literature. This is achieved by direct summation or the constant term method. We also obtain some new single-sum identities as consequences.