A further look at the truncated pentagonal number theorem

Abstract

In this paper, we study the asymptotic behavior of the following function $$M_k(n):=(-1{)}^{k-1}\sum _{j=0}^{k-1}(p(n-j(3j+1)/2)-p(n-j(3j+5)/2-1)),$$ which arises from Andrews and Merca's truncated pentagonal number theorem.