Fungrim entry: 51fd98

\zeta\!\left(-n\right) = \frac{{\left(-1\right)}^{n} B_{n + 1}}{n + 1}

Assumptions:

n \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
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`Pow`	${a}^{b}$	Power
`BernoulliB`	$B_{n}$	Bernoulli number
`ZZ`	$\mathbb{Z}$	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

Riemann zeta function

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