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Fungrim entry: fa9b71

∣atan⁡(z)∣≤−log⁡ ⁣(1−∣z∣)\left|\operatorname{atan}(z)\right| \le -\log\!\left(1 - \left|z\right|\right)
Assumptions:z∈C  and⁡  ∣z∣≤1z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \le 1
TeX:
\left|\operatorname{atan}(z)\right| \le -\log\!\left(1 - \left|z\right|\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \le 1
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
Loglog⁡(z)\log(z) Natural logarithm
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("fa9b71"),
    Formula(LessEqual(Abs(Atan(z)), Neg(Log(Sub(1, Abs(z)))))),
    Variables(z),
    Assumptions(And(Element(z, CC), LessEqual(Abs(z), 1))))

Topics using this entry

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