Approximate Formula for Number of Partitions

Theorem

The number of partitions $\map p n$ of a (strictly) positive integer $n$ is given by the approximation:

$\map p n \approx \dfrac {e^{\pi \sqrt {2 n / 3} } } {4 n \sqrt 3}$


Proof


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Sources

  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$): Footnote $7$
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