Fungrim entry: ad269f

\left(s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) < 0 \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{C}

TeX:

\left(s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) < 0 \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`CC`	$\mathbb{C}$	Complex numbers
`Re`	$\operatorname{Re}(z)$	Real part
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function

Source code for this entry:

Entry(ID("ad269f"),
    Formula(Implies(And(Element(s, CC), Less(Re(s), 0), Element(a, CC)), Element(HurwitzZeta(s, a), CC))),
    Variables(s, a))

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