$q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type

Abstract

In a recent paper, I defined the "standard multiparameter Bailey pair" (SMPBP) and demonstrated that all of the classical Bailey pairs considered by W.N. Bailey in his famous paper (Proc. London Math. Soc. (2), 50 (1948), 1--10) arose as special cases of the SMPBP. Additionally, I was able to find a number of new Rogers-Ramanujan type identities. From a given Bailey pair, normally only one or two Rogers-Ramanujan type identities follow immediately. In this present work, I present the set of $q$-difference equations associated with the SMPBP, and use these $q$-difference equations to deduce the complete families of Rogers-Ramanujan type identities.