Multidimensional Rogers-Ramanujan type identities with parameters

TL;DR

This paper develops a contour integral approach to derive multidimensional Rogers-Ramanujan type identities with parameters, generalizing existing results and introducing new triple-sum identities.

Contribution

It introduces a reduction formula from double to single series with parameters, unifies several known results, and presents new multidimensional identities.

Findings

Derived a reduction formula connecting double and single series.

Unified and extended previous Rogers-Ramanujan type identities.

Discovered new triple-sum generalizations of known formulas.

Abstract

Via the contour integral method, we establish a reduction formula from a double series to a single series with parameters, which not only implies Uncu and Zudilin's two results and Cao and Wang's two results, but also is related to Berkovich and Warnaar's equation. Similarly, we also discover some triple-sum generalizations of Cao and Wang's formulas. As conclusions, several multidimensional Rogers--Ramanujan type identities with parameters or without parameters are given.