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Fungrim entry: 8f5e66

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

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

2019-08-17 11:32:46.829430 UTC