Fungrim home page

Fungrim entry: 12765e

atan⁡(z)=−i2log⁡ ⁣(1+iz1−iz)\operatorname{atan}(z) = -\frac{i}{2} \log\!\left(\frac{1 + i z}{1 - i z}\right)
Assumptions:z∈C  and⁡  zi∉[1,∞)z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z i \notin \left[1, \infty\right)
TeX:
\operatorname{atan}(z) = -\frac{i}{2} \log\!\left(\frac{1 + i z}{1 - i z}\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z i \notin \left[1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
ConstIii Imaginary unit
Loglog⁡(z)\log(z) Natural logarithm
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("12765e"),
    Formula(Equal(Atan(z), Mul(Neg(Div(ConstI, 2)), Log(Div(Add(1, Mul(ConstI, z)), Sub(1, Mul(ConstI, z))))))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(Mul(z, ConstI), ClosedOpenInterval(1, Infinity)))))

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