Fungrim entry: 8f5e66

\zeta\!\left(s\right) = \prod_{p} \frac{1}{1 - \frac{1}{{p}^{s}}}

Assumptions:

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1

TeX:

\zeta\!\left(s\right) = \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
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`PrimeProduct`	$\prod_{p} f(p)$	Product over primes
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`Re`	$\operatorname{Re}(z)$	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))))

Topics using this entry

Riemann zeta function

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