Truncated sums for Hecke-Rogers type identities and Andrews-Hickerson's Bailey pair

Abstract

Recently, Wang and Yee proved three truncated sums for some Hecke-Rogers type identities. Motivated by the work of Wang and Yee, we derive five new Hecke-Rogers type identities and pose their truncated sums based on Andrews-Hickerson's Bailey pair and a lemma given by Wang and Yee in this paper. As applications, we deduce several infinite families of linear inequalities for certain restricted partition functions. Additionally, we provide a unified treatment of some truncated identities due to Wang-Yee and He by employing Andrews-Hickerson's Bailey pair.