Some implications of the $2$-fold Bailey lemma

Abstract

The $2$-fold Bailey lemma is a special case of the $s$-fold Bailey lemma introduced by Andrews in 2000. We examine this special case and its applications to partitions and recently discovered $q$-series identities. Our work provides a general comparison of the utility of the $2$-fold Bailey lemma and the more widely applied $1$-fold Bailey lemma. We also offer a discussion of the $sp{t}_M(n)$ function and related identities.

Major revision

References in corpus (2)

• Bailey Type Transforms and Applications
• The tri-pentagonal number theorem and related identities

Cited by in corpus (2)

• An interesting $q$-series related to the 4-th symmetrized rank function
• On an spt function for the $4$-th symmetrized crank function