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Fungrim entry: 69ca86

B2n>4πn(nπe)2n\left|B_{2 n}\right| > 4 \sqrt{\pi n} {\left(\frac{n}{\pi e}\right)}^{2 n}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
\left|B_{2 n}\right| > 4 \sqrt{\pi n} {\left(\frac{n}{\pi e}\right)}^{2 n}

n \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
BernoulliBBnB_{n} Bernoulli number
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
ConstEee The constant e (2.718...)
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Greater(Abs(BernoulliB(Mul(2, n))), Mul(Mul(4, Sqrt(Mul(Pi, n))), Pow(Div(n, Mul(Pi, ConstE)), Mul(2, n))))),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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

2020-08-27 09:56:25.682319 UTC