Identities of the Rogers--Ramanujan--Slater Type

Abstract

It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers-Ramanujan identities (L. J. Slater, Further identities of the Rogers-Ramanujan type, \emph{Proc. London Math Soc. (2)} \textbf{54} (1952), 147--167) can be easily derived using just three multiparameter Bailey pairs and their associated $q$-difference equations. As a bonus, new Rogers-Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.

arXiv comment28 pages

References in corpus (3)

• On identities of the Rogers--Ramanujan type
• $q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type
• Identities of the Rogers--Ramanujan--Bailey Type

Cited by in corpus (5)

• Ghost series and a motivated proof of the Andrews-Bressoud identities
• Lifting Bailey Pairs to WP-Bailey Pairs
• Bailey Type Transforms and Applications
• A partition bijection related to the Rogers--Selberg identities and Gordon's theorem
• Several new product identities in relation to two-variable Rogers-Ramanujan type sums and mock theta functions