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Fungrim entry: 1d46d4

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

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2019-06-18 07:49:59.356594 UTC