A further look at the truncated pentagonal number theorem

Shane Chern

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arXiv · 1808.00227

A further look at the truncated pentagonal number theorem

Shane Chern

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Abstract

In this paper, we study the asymptotic behavior of the following 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.

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Shane Chern. 2018-08-01. A further look at the truncated pentagonal number theorem. https://arxiv.org/abs/1808.00227

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