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Fungrim entry: 3b11d3

BranchCuts ⁣(atan(z),z,C)={(,1]i,[1,)i}\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
Atanatan(z)\operatorname{atan}(z) 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)))))

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

2020-01-31 18:09:28.494564 UTC