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Fungrim entry: 7272a8

∣atan⁡(z)∣≤∣atanh⁡ ⁣(∣z∣)∣\left|\operatorname{atan}(z)\right| \le \left|\operatorname{atanh}\!\left(\left|z\right|\right)\right|
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\left|\operatorname{atan}(z)\right| \le \left|\operatorname{atanh}\!\left(\left|z\right|\right)\right|

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("7272a8"),
    Formula(LessEqual(Abs(Atan(z)), Abs(Atanh(Abs(z))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC