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arXiv · 2302.03835

Rademacher's Formula for the Partition Function

Ze-Yong Kong·Lee-Peng Teo
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Abstract

For a positive integer $n$, let $p(n)$ be the number of ways to express $n$ as a sum of positive integers. In this note, we revisit the derivation of the Rademacher's convergent series for $p(n)$ in a pedagogical way, with all the details given. We also derive the leading asymptotic behavior of $p(n)$ when $n$ approaches infinity. Some numerical results are tabled.

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Ze-Yong Kong, Lee-Peng Teo. 2023-02-08. Rademacher's Formula for the Partition Function. https://arxiv.org/abs/2302.03835

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