Bilateral identities of the Rogers-Ramanujan type

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 Bressoud's even modulus identities, and other identities. The here revealed closed form bilateral and multilateral summations appear to be the very first of their kind. Given that the classical Rogers-Ramanujan identities have well-established connections to various areas in mathematics and in physics, it is natural to expect that the new bilateral and multilateral identities can be similarly connected to those areas. This is supported by concrete combinatorial interpretations for a collection of four bilateral companions to the classical Rogers-Ramanujan identities.Comment: 25 page

Andrews Style Partition Identities

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations which are satisfied by the generating functions. In contrast, the conventional approach is to show that a variant of well-known series satisfies the system of functional equations, thus reconciling two separate lines of computations

An A2_2 Bailey lemma and Rogers--Ramanujan-type identities

Using new $q$-functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A_2 version of the classical Bailey lemma. We apply our result, which is distinct from the A_2 Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W_3 algebra.Comment: AMS-LaTeX, 25 page