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

Hurwitz 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