Fungrim entry: 7697af

p\!\left(n\right) \sim \frac{{e}^{\pi \sqrt{2 n / 3}}}{4 n \sqrt{3}}, \; n \to \infty

Assumptions:

n \in \mathbb{Z}

TeX:

p\!\left(n\right) \sim \frac{{e}^{\pi \sqrt{2 n / 3}}}{4 n \sqrt{3}}, \; n \to \infty

n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`PartitionsP`	$p\!\left(n\right)$	Integer partition function
`Exp`	${e}^{z}$	Exponential function
`ConstPi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`Infinity`	$\infty$	Positive infinity
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("7697af"),
    Formula(AsymptoticTo(PartitionsP(n), Div(Exp(Mul(ConstPi, Sqrt(Div(Mul(2, n), 3)))), Mul(Mul(4, n), Sqrt(3))), n, Infinity)),
    Variables(n),
    Assumptions(Element(n, ZZ)))

Topics using this entry

Partition function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC