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

n \in \mathbb{Z}
Fungrim symbol Notation Short description
PartitionsPp(n)p(n) Integer partition function
Expez{e}^{z} Exponential function
Piπ\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:
    Formula(AsymptoticTo(PartitionsP(n), Div(Exp(Mul(Pi, Sqrt(Div(Mul(2, n), 3)))), Mul(Mul(4, n), Sqrt(3))), n, Infinity)),
    Assumptions(Element(n, ZZ)))

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2021-03-15 19:12:00.328586 UTC