# Fungrim entry: 90a864

$\operatorname{atan}(z) = \int_{0}^{z} \frac{1}{1 + {t}^{2}} \, dt$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; i z \notin \left(-\infty, -1\right] \cup \left[1, \infty\right)$
TeX:
\operatorname{atan}(z) = \int_{0}^{z} \frac{1}{1 + {t}^{2}} \, dt

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; i z \notin \left(-\infty, -1\right] \cup \left[1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atan$\operatorname{atan}(z)$ Inverse tangent
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ConstI$i$ Imaginary unit
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Source code for this entry:
Entry(ID("90a864"),
Formula(Equal(Atan(z), Integral(Div(1, Add(1, Pow(t, 2))), For(t, 0, z)))),
Variables(z),
Assumptions(And(Element(z, CC), NotElement(Mul(ConstI, z), Union(OpenClosedInterval(Neg(Infinity), -1), 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