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On Bilateral Multiple Sums and Rogers-Ramanujan Type Identities

Dandan Chen, Tianjian Xu

Abstract

We establish a new bilateral double-sum Rogers-Ramanujan identity involving two parameters. As applications, this identity yields several new multi-sum Rogers-Ramanujan type identities. Our proofs utilize the theory of basic hypergeometric series in conjunction with the integral method.

On Bilateral Multiple Sums and Rogers-Ramanujan Type Identities

Abstract

We establish a new bilateral double-sum Rogers-Ramanujan identity involving two parameters. As applications, this identity yields several new multi-sum Rogers-Ramanujan type identities. Our proofs utilize the theory of basic hypergeometric series in conjunction with the integral method.
Paper Structure (3 sections, 2 theorems, 26 equations)

This paper contains 3 sections, 2 theorems, 26 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Proof of Theorem \ref{['main-theorem']} and Corollary \ref{['cor']}

Key Result

Theorem 1.1

We have

Theorems & Definitions (5)

  • Theorem 1.1
  • Corollary 1.2
  • Remark 1.3
  • proof : The proof of Theorem \ref{['main-theorem']}
  • proof : The proof of Corollary \ref{['cor']}