Difference between revisions of "Asymptotic formula for partition function"

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(Created page with "==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 partiti...")
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Revision as of 20:49, 26 June 2016

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.

Proof

References