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Fungrim entry: 8f5e66

ζ(s)=p111ps\zeta(s) = \prod_{p} \frac{1}{1 - \frac{1}{{p}^{s}}}
Assumptions:sCandRe(s)>1s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(s) > 1
TeX:
\zeta(s) = \prod_{p} \frac{1}{1 - \frac{1}{{p}^{s}}}

s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(s) > 1
Definitions:
Fungrim symbol Notation Short description
RiemannZetaζ(s)\zeta(s) Riemann zeta function
PrimeProductpf(p)\prod_{p} f(p) Product over primes
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
Entry(ID("8f5e66"),
    Formula(Equal(RiemannZeta(s), PrimeProduct(Div(1, Sub(1, Div(1, Pow(p, s)))), For(p)))),
    Variables(s),
    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.

2019-10-05 13:11:19.856591 UTC