Fungrim entry: 3b11d3

\operatorname{BranchCuts}\!\left(\operatorname{atan}(z), z, \mathbb{C}\right) = \left\{\left(-\infty, -1\right] i, \left[1, \infty\right) i\right\}

TeX:

\operatorname{BranchCuts}\!\left(\operatorname{atan}(z), z, \mathbb{C}\right) = \left\{\left(-\infty, -1\right] i, \left[1, \infty\right) i\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity
`ConstI`	$i$	Imaginary unit
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval

Source code for this entry:

Entry(ID("3b11d3"),
    Formula(Equal(BranchCuts(Atan(z), z, CC), Set(Mul(OpenClosedInterval(Neg(Infinity), -1), ConstI), Mul(ClosedOpenInterval(1, Infinity), ConstI)))))

Topics using this entry

Inverse tangent

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