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Fungrim entry: a3a253

log⁡ ⁣(ez)=z−2πi⌈Im⁡(z)2π−12⌉\log\!\left({e}^{z}\right) = z - 2 \pi i \left\lceil \frac{\operatorname{Im}(z)}{2 \pi} - \frac{1}{2} \right\rceil
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\log\!\left({e}^{z}\right) = z - 2 \pi i \left\lceil \frac{\operatorname{Im}(z)}{2 \pi} - \frac{1}{2} \right\rceil

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Loglog⁡(z)\log(z) Natural logarithm
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
ImIm⁡(z)\operatorname{Im}(z) Imaginary part
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("a3a253"),
    Formula(Equal(Log(Exp(z)), Sub(z, Mul(Mul(Mul(2, Pi), ConstI), Ceil(Sub(Div(Im(z), Mul(2, Pi)), Div(1, 2))))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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