# Approximate Formula for Number of Partitions

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## 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

## Sources

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