# Fungrim entry: 6e69fc

$\zeta\!\left(s, n\right) = \zeta\!\left(s\right) - \sum_{k=1}^{n - 1} \frac{1}{{k}^{s}}$
Assumptions:$s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}$
TeX:
\zeta\!\left(s, n\right) = \zeta\!\left(s\right) - \sum_{k=1}^{n - 1} \frac{1}{{k}^{s}}

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
HurwitzZeta$\zeta\!\left(s, a\right)$ Hurwitz zeta function
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("6e69fc"),
Formula(Equal(HurwitzZeta(s, n), Sub(RiemannZeta(s), Sum(Div(1, Pow(k, s)), For(k, 1, Sub(n, 1)))))),
Variables(s, n),
Assumptions(And(Element(s, CC), Element(n, ZZGreaterEqual(1)))))

## Topics using this entry

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