# Fungrim entry: 1d46d4

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

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

2021-03-15 19:12:00.328586 UTC