Methods and Applications of Analysis

Volume 27 (2020)

Number 2

Some implications of the $2$-fold Bailey lemma

Pages: 153 – 160



Alexander E. Patkowski (Centerville, Massachusetts, U.S.A.)


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.


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