Fungrim entry: a18b77

\operatorname{atan}(z) = \frac{i}{2} \left(\log\!\left(1 - i z\right) - \log\!\left(1 + i z\right)\right)

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{atan}(z) = \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
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`ConstI`	$i$	Imaginary unit
`Log`	$\log(z)$	Natural logarithm
`CC`	$\mathbb{C}$	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

Inverse tangent

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