Multiple series Rogers-Ramanujan type identities

Abstract

It is shown how each of the classical identities of Rogers-Ramanujan type can be embedded in an infinite family of multiple series identities. The method of construction is applied to four of L. J. Rogers' elegant series related to the quintuple product identity. Other applications are also presented.

Bailey Pairs With Free Parameters, Mock Theta Functions and Tubular Partitions

“…This seems to be highly unlikely in general given the right-hand side of (1.5). However, as was shown in [2], [3] there is as equivalent formulation of the defining relation between α(a, n) and β n :…”

The Bailey transform and false theta functions

“…Before proceeding we remark that the Bailey pair (4.1) may readily be related to the more standard definition of such pairs [2,3,17]. Specifically, if we define α 0 = α 0 and, for n > 0, α n = α n + α −n , then (α n , β n ) is a Bailey pair with a = 1 and q → q 2 .…”

“…Specifically, if we define α 0 = α 0 and, for n > 0, α n = α n + α −n , then (α n , β n ) is a Bailey pair with a = 1 and q → q 2 . From this comment it follows that we may utilize L. J. Slater's compendium of Bailey pairs [14], as well as other sources [5,2], to obtain false theta identities.…”

“…In light of the enormous number of known Bailey pairs (c.f. [2,5]), we will only provide a minimal sample in this section.…”

Non-unitary minimal models, Bailey's Lemma and N=1,2 Superconformal algebras

“…In this section we summarize Bailey's original lemma [2,3] and the Bose-Fermi identities for the M (p, p ′ ) minimal models [5,6,16,26].…”