Rademacher's Formula for the Partition Function

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.