Fungrim home page

Fungrim entry: 69ca86

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

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
BernoulliBBnB_{n} Bernoulli number
Sqrtz\sqrt{z} Principal square root
ConstPiπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
ConstEee The constant e (2.718...)
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("69ca86"),
    Formula(Greater(Abs(BernoulliB(Mul(2, n))), Mul(Mul(4, Sqrt(Mul(ConstPi, n))), Pow(Div(n, Mul(ConstPi, ConstE)), Mul(2, n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

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