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Fungrim entry: 1d46d4

1ζ(s)=k=1μ(k)ks\frac{1}{\zeta(s)} = \sum_{k=1}^{\infty} \frac{\mu(k)}{{k}^{s}}
Assumptions:sCandRe(s)>1s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(s) > 1
\frac{1}{\zeta(s)} = \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(s) 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))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC