On Bilateral Multiple Sums and Rogers-Ramanujan Type Identities

TL;DR

This paper introduces new bilateral double-sum Rogers-Ramanujan identities with parameters, leading to multiple new multi-sum identities, using hypergeometric series theory and integral methods.

Contribution

It presents novel bilateral double-sum Rogers-Ramanujan identities and their applications to derive several new multi-sum identities.

Findings

Established new bilateral double-sum Rogers-Ramanujan identities.

Derived multiple new multi-sum Rogers-Ramanujan type identities.

Utilized hypergeometric series and integral methods in proofs.

Abstract

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