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 Göllnitz–Gordon identities, and of related identities by Ramanujan, Jackson, and Slater. We give corresponding results for multisums including multilateral extensions of the Andrews–Gordon identities, of the Andrews–Bressoud generalization of the Göllnitz–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.