A further look at the truncated pentagonal number theorem
Volume 189 / 2019
Acta Arithmetica 189 (2019), 397-403
MSC: Primary 11P82; Secondary 05A17.
DOI: 10.4064/aa180718-6-11
Published online: 7 June 2019
Abstract
We study the asymptotic behavior of the function $$ M_k(n):=(-1)^{k-1} \sum_{j=0}^{k-1}\big(p(n-j(3j+1)/2)-p(n-j(3j+5)/2-1)\big), $$ which arises from Andrews and Merca’s truncated pentagonal number theorem.
