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Fungrim entry: a18b77

atan⁡ ⁣(z)=i2(log⁡ ⁣(1−iz)−log⁡ ⁣(1+iz))\operatorname{atan}\!\left(z\right) = \frac{i}{2} \left(\log\!\left(1 - i z\right) - \log\!\left(1 + i z\right)\right)
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\operatorname{atan}\!\left(z\right) = \frac{i}{2} \left(\log\!\left(1 - i z\right) - \log\!\left(1 + i z\right)\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Atanatan⁡ ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
ConstIii Imaginary unit
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("a18b77"),
    Formula(Equal(Atan(z), Mul(Div(ConstI, 2), Sub(Log(Sub(1, Mul(ConstI, z))), Log(Add(1, Mul(ConstI, z))))))),
    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.

2019-06-18 07:49:59.356594 UTC