Multi-sum Rogers-Ramanujan Type Identities

TL;DR

This paper introduces an integral method to prove Rogers-Ramanujan type identities involving multiple sums, expanding the toolkit for discovering and verifying complex q-series identities.

Contribution

It presents a novel integral approach inspired by Rosengren's proof techniques to establish new Rogers-Ramanujan type identities with double and triple sums.

Findings

Derived new Rogers-Ramanujan type identities

Demonstrated the effectiveness of integral methods for complex q-series

Connected integral contours to infinite product identities

Abstract

We use an integral method to establish a number of Rogers-Ramanujan type identities involving double and triple sums. The key step for proving such identities is to find some infinite products whose integrals over suitable contours are still infinite products. The method used here is motivated by Rosengren's proof of the Kanade-Russell identities.