Fungrim entry: 0bd6aa

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

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1 \;\mathbin{\operatorname{and}}\; N \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
HurwitzZeta$\zeta\!\left(s, a\right)$ Hurwitz zeta function
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("0bd6aa"),
Formula(Equal(HurwitzZeta(s, N), Sum(Div(1, Pow(n, s)), For(n, N, Infinity)))),
Variables(s, N),
Assumptions(And(Element(s, CC), Greater(Re(s), 1), 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