Bilateral identities of the Rogers--Ramanujan type

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.