Fungrim entry: 4e5947

\operatorname{atan}(z) = \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}(z) = \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`	$\operatorname{atan}(z)$	Inverse tangent
`Sum`	$\sum_{n} f(n)$	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)), For(k, 0, Infinity)))),
    Variables(z),
    Assumptions(And(Element(z, CC), Less(Abs(z), 1))))

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