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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==Theorem== | ==Theorem== | ||
| − | The following asymptotic formula holds: | + | The following [[asymptotic formula]] holds: |
$$p(n) \sim \dfrac{1}{4n\sqrt{3}} \exp \left( \pi \sqrt{ \dfrac{2}{3} } \sqrt{n} \right),$$ | $$p(n) \sim \dfrac{1}{4n\sqrt{3}} \exp \left( \pi \sqrt{ \dfrac{2}{3} } \sqrt{n} \right),$$ | ||
where $p$ denotes the [[partition]] function, $\exp$ denotes the [[exponential]], and $\pi$ denotes [[pi]]. | where $p$ denotes the [[partition]] function, $\exp$ denotes the [[exponential]], and $\pi$ denotes [[pi]]. | ||
Latest revision as of 00:10, 28 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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.2.1 \mathrm{III}$
