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Fungrim entry: 3a1316

∣B2n∣<(1+1n)4πn(nπe)2n\left|B_{2 n}\right| < \left(1 + \frac{1}{n}\right) 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| < \left(1 + \frac{1}{n}\right) 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
Piπ\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("3a1316"),
    Formula(Less(Abs(BernoulliB(Mul(2, n))), Mul(Mul(Mul(Add(1, Div(1, n)), 4), Sqrt(Mul(Pi, n))), Pow(Div(n, Mul(Pi, ConstE)), Mul(2, n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC