Fungrim home page

Fungrim entry: 3b11d3

BranchCuts ⁣(atan ⁣(z),z,C)={(,1]i,[1,)i}\operatorname{BranchCuts}\!\left(\operatorname{atan}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, -1\right] i, \left[1, \infty\right) i\right\}
TeX:
\operatorname{BranchCuts}\!\left(\operatorname{atan}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, -1\right] i, \left[1, \infty\right) i\right\}
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
ConstIii Imaginary unit
ClosedOpenInterval[a,b)\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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-16 21:17:18.797188 UTC