Fungrim home page

Fungrim entry: 1d46d4

1ζ ⁣(s)=k=1μ(k)ks\frac{1}{\zeta\!\left(s\right)} = \sum_{k=1}^{\infty} \frac{\mu(k)}{{k}^{s}}
Assumptions:sC  and  Re(s)>1s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1
\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
Fungrim symbol Notation Short description
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Sumnf(n)\sum_{n} f(n) Sum
MoebiusMuμ(n)\mu(n) Möbius function
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
    Formula(Equal(Div(1, RiemannZeta(s)), Sum(Div(MoebiusMu(k), Pow(k, s)), For(k, 1, Infinity)))),
    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