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Fungrim entry: 792c76

∣log⁡ ⁣(z)∣≤∣log⁡ ⁣(∣z∣)∣+π\left|\log\!\left(z\right)\right| \le \left|\log\!\left(\left|z\right|\right)\right| + \pi
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\left|\log\!\left(z\right)\right| \le \left|\log\!\left(\left|z\right|\right)\right| + \pi

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("792c76"),
    Formula(LessEqual(Abs(Log(z)), Add(Abs(Log(Abs(z))), ConstPi))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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

2019-06-18 07:49:59.356594 UTC