Fungrim entry: e7224b

\left(s \in \mathbb{R} \setminus \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \left(0, \infty\right)\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{R}

TeX:

\left(s \in \mathbb{R} \setminus \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \left(0, \infty\right)\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`RR`	$\mathbb{R}$	Real numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function

Source code for this entry:

Entry(ID("e7224b"),
    Formula(Implies(And(Element(s, SetMinus(RR, Set(1))), Element(a, OpenInterval(0, Infinity))), Element(HurwitzZeta(s, a), RR))),
    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