# Fungrim entry: 1d46d4

$\frac{1}{\zeta\!\left(s\right)} = \sum_{k=1}^{\infty} \frac{\mu\!\left(k\right)}{{k}^{s}}$
Assumptions:$s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(s\right) > 1$
TeX:
\frac{1}{\zeta\!\left(s\right)} = \sum_{k=1}^{\infty} \frac{\mu\!\left(k\right)}{{k}^{s}}

s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(s\right) > 1
Definitions:
Fungrim symbol Notation Short description
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
Sum$\sum_{n} f\!\left(n\right)$ Sum
MoebiusMu$\mu\!\left(n\right)$ Möbius function
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}\!\left(z\right)$ Real part
Source code for this entry:
Entry(ID("1d46d4"),
Formula(Equal(Div(1, RiemannZeta(s)), Sum(Div(MoebiusMu(k), Pow(k, s)), Tuple(k, 1, Infinity)))),
Variables(s),
Assumptions(And(Element(s, CC), Greater(Re(s), 1))))

## 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