Bilateral identities of the Rogers--Ramanujan type

TL;DR

This paper analytically derives new bilateral and multilateral identities of the Rogers--Ramanujan type, extending classical identities and providing potentially first-of-their-kind closed-form bilateral and multilateral summations.

Contribution

It introduces the first known closed-form bilateral and multilateral summations of Rogers--Ramanujan type identities, extending several classical identities in the literature.

Findings

Derived bilateral extensions of Rogers--Ramanujan and G"ollnitz-Gordon identities.

Extended identities by Ramanujan, Jackson, and Slater to bilateral forms.

Presented multilateral extensions of Andrews--Gordon and Bressoud identities.

Abstract

We derive by analytic means a number of bilateral identities of the Rogers--Ramanujan type. Our results include bilateral extensions of the Rogers--Ramanujan and the G\"ollnitz-Gordon identities, and of related identities by Ramanujan, Jackson, and Slater. We give corresponding results for multiseries including multilateral extensions of the Andrews--Gordon identities, of the Andrews--Bressoud generalization of the G\"ollnitz--Gordon identities, of Bressoud's even modulus identities, and other identities. Our closed form bilateral and multilateral summations appear to be the very first of their kind.