# Fungrim entry: 14ecc4

$B_{2 n} = {\left(-1\right)}^{n + 1} \frac{2 \left(2 n\right)! \zeta\!\left(2 n\right)}{{\left(2 \pi\right)}^{2 n}}$
Assumptions:$n \in \mathbb{Z}_{\ge 1}$
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
BernoulliB$B_{n}$ Bernoulli number
Pow${a}^{b}$ Power
Factorial$n !$ Factorial
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
Pi$\pi$ The constant pi (3.14...)
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ 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, Pi), 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.

2021-03-15 19:12:00.328586 UTC