# Fungrim entry: 1a907e

$\sum_{n=1}^{\infty} \frac{\varphi(n)}{{n}^{s}} = \frac{\zeta\!\left(s - 1\right)}{\zeta\!\left(s\right)}$
Assumptions:$s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 2$
TeX:
\sum_{n=1}^{\infty} \frac{\varphi(n)}{{n}^{s}} = \frac{\zeta\!\left(s - 1\right)}{\zeta\!\left(s\right)}

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 2
Definitions:
Fungrim symbol Notation Short description
Sum$\sum_{n} f(n)$ Sum
Totient$\varphi(n)$ Euler totient function
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("1a907e"),
Formula(Equal(Sum(Div(Totient(n), Pow(n, s)), For(n, 1, Infinity)), Div(RiemannZeta(Sub(s, 1)), RiemannZeta(s)))),
Variables(s),
Assumptions(And(Element(s, CC), Greater(Re(s), 2))))

## Topics using this entry

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

2020-08-27 09:56:25.682319 UTC