Infinite families of Hecke-Rogers type series and their truncated representations

Abstract

Recently, Andrews and Merca studied the truncated version of Euler's pentagonal number theorem. Their work opened up a new study on truncated series. Since then, many truncated versions of theta series have been discovered. Very recently, Wang and Yee generalized the study on truncated series to Hecke-Rogers type series and obtained three new truncated Hecke-Rogers series. Inspired by these works, we not only prove several infinite families of Hecke-Rogers type series and their truncated versions, but also establish some inequalities on some interesting partition functions in this paper. In particular, we generalize some results due to Wang and Yee, and He. Our work mainly relies on some formulas on the evaluation of certain terminating basic hypergeometric ϕ23 series.