Fungrim home page

Fungrim entry: 7dab87

ζ ⁣(−n,0)=−Bn+1n+1\zeta\!\left(-n, 0\right) = -\frac{B_{n + 1}}{n + 1}
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
\zeta\!\left(-n, 0\right) = -\frac{B_{n + 1}}{n + 1}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
BernoulliBBnB_{n} Bernoulli number
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("7dab87"),
    Formula(Equal(HurwitzZeta(Neg(n), 0), Neg(Div(BernoulliB(Add(n, 1)), Add(n, 1))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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