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Fungrim entry: 14ecc4

B2n=(1)n+12(2n)!ζ ⁣(2n)(2π)2nB_{2 n} = {\left(-1\right)}^{n + 1} \frac{2 \left(2 n\right)! \zeta\!\left(2 n\right)}{{\left(2 \pi\right)}^{2 n}}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
TeX:
B_{2 n} = {\left(-1\right)}^{n + 1} \frac{2 \left(2 n\right)! \zeta\!\left(2 n\right)}{{\left(2 \pi\right)}^{2 n}}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
BernoulliBBnB_{n} Bernoulli number
Powab{a}^{b} Power
Factorialn!n ! Factorial
RiemannZetaζ(s)\zeta(s) Riemann zeta function
ConstPiπ\pi The constant pi (3.14...)
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("14ecc4"),
    Formula(Equal(BernoulliB(Mul(2, n)), Mul(Pow(-1, Add(n, 1)), Div(Mul(Mul(2, Factorial(Mul(2, n))), RiemannZeta(Mul(2, n))), Pow(Mul(2, ConstPi), Mul(2, n)))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2019-10-05 13:11:19.856591 UTC