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Fungrim entry: 0f02a5

B2n<(1+1n)2(2n)!(2π)2n\left|B_{2 n}\right| < \left(1 + \frac{1}{n}\right) \frac{2 \left(2 n\right)!}{{\left(2 \pi\right)}^{2 n}}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
\left|B_{2 n}\right| < \left(1 + \frac{1}{n}\right) \frac{2 \left(2 n\right)!}{{\left(2 \pi\right)}^{2 n}}

n \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
BernoulliBBnB_{n} Bernoulli number
Factorialn!n ! Factorial
Powab{a}^{b} Power
Piπ\pi The constant pi (3.14...)
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Less(Abs(BernoulliB(Mul(2, n))), Mul(Add(1, Div(1, n)), Div(Mul(2, Factorial(Mul(2, n))), Pow(Mul(2, Pi), Mul(2, n)))))),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC