Contents Online
Methods and Applications of Analysis
Volume 27 (2020)
Number 2
Some implications of the $2$-fold Bailey lemma
Pages: 153 – 160
DOI: https://dx.doi.org/10.4310/MAA.2020.v27.n2.a3
Author
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 $\operatorname{spt}_M (n)$ function and related identities.
Keywords
partitions, $q$-series, Bailey’s lemma
2010 Mathematics Subject Classification
Primary 11P81. Secondary 11P83.
Received 12 December 2019
Accepted 23 July 2020
Published 20 August 2020