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Fungrim entry: 7697af

p(n)eπ2n/34n3,  np(n) \sim \frac{{e}^{\pi \sqrt{2 n / 3}}}{4 n \sqrt{3}}, \; n \to \infty
Assumptions:nZn \in \mathbb{Z}
TeX:
p(n) \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
PartitionsPp(n)p(n) Integer partition function
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
Infinity\infty Positive infinity
ZZZ\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)))

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

2019-10-05 13:11:19.856591 UTC