Asymptotic formula for partition function

Theorem

The following asymptotic formula holds: $$p(n) \sim \dfrac{1}{4n\sqrt{3}} \exp \left( \pi \sqrt{ \dfrac{2}{3} } \sqrt{n} \right),$$ where $p$ denotes the partition function, $\exp$ denotes the exponential, and $\pi$ denotes pi.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.2.1 \mathrm{III}$