Fungrim home page

Fungrim entry: 51fd98

ζ ⁣(n)=(1)nBn+1n+1\zeta\!\left(-n\right) = \frac{{\left(-1\right)}^{n} B_{n + 1}}{n + 1}
Assumptions:nZandn0n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ge 0
TeX:
\zeta\!\left(-n\right) = \frac{{\left(-1\right)}^{n} B_{n + 1}}{n + 1}

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ge 0
Definitions:
Fungrim symbol Notation Short description
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Powab{a}^{b} Power
BernoulliBBnB_{n} Bernoulli number
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("51fd98"),
    Formula(Equal(RiemannZeta(Neg(n)), Div(Mul(Pow(-1, n), BernoulliB(Add(n, 1))), Add(n, 1)))),
    Variables(n),
    Assumptions(And(Element(n, ZZ), GreaterEqual(n, 0))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-17 11:32:46.829430 UTC