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Fungrim entry: 0f02a5

∣B2n∣<(1+1n)2(2n)!(2π)2n\left|B_{2 n}\right| \lt \left(1 + \frac{1}{n}\right) \frac{2 \left(2 n\right)!}{{\left(2 \pi\right)}^{2 n}}
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\left|B_{2 n}\right| \lt \left(1 + \frac{1}{n}\right) \frac{2 \left(2 n\right)!}{{\left(2 \pi\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
Factorialn!n ! Factorial
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("0f02a5"),
    Formula(Less(Abs(BernoulliB(Mul(2, n))), Mul(Add(1, Div(1, n)), Div(Mul(2, Factorial(Mul(2, n))), Pow(Mul(2, ConstPi), Mul(2, n)))))),
    Variables(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.

2019-06-18 07:49:59.356594 UTC