# Fungrim entry: 4e5947

$\operatorname{atan}\!\left(z\right) = \sum_{k=0}^{\infty} \frac{{\left(-1\right)}^{k} {z}^{2 k + 1}}{2 k + 1}$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < 1$
TeX:
\operatorname{atan}\!\left(z\right) = \sum_{k=0}^{\infty} \frac{{\left(-1\right)}^{k} {z}^{2 k + 1}}{2 k + 1}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < 1
Definitions:
Fungrim symbol Notation Short description
Atan$\operatorname{atan}\!\left(z\right)$ Inverse tangent
Sum$\sum_{n} f\!\left(n\right)$ Sum
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Abs$\left|z\right|$ Absolute value
Source code for this entry:
Entry(ID("4e5947"),
Formula(Equal(Atan(z), Sum(Div(Mul(Pow(-1, k), Pow(z, Add(Mul(2, k), 1))), Add(Mul(2, k), 1)), Tuple(k, 0, Infinity)))),
Variables(z),
Assumptions(And(Element(z, CC), Less(Abs(z), 1))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-20 18:07:53.062439 UTC