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

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