# Fungrim entry: 3478af

$\operatorname{atan}(x) \le \sum_{k=0}^{2 N} \frac{{\left(-1\right)}^{k} {x}^{2 k + 1}}{2 k + 1}$
Assumptions:$x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; N \in \mathbb{Z}_{\ge 0}$
TeX:
\operatorname{atan}(x) \le \sum_{k=0}^{2 N} \frac{{\left(-1\right)}^{k} {x}^{2 k + 1}}{2 k + 1}

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; N \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Atan$\operatorname{atan}(z)$ Inverse tangent
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("3478af"),
Formula(LessEqual(Atan(x), Sum(Div(Mul(Pow(-1, k), Pow(x, Add(Mul(2, k), 1))), Add(Mul(2, k), 1)), For(k, 0, Mul(2, N))))),
Variables(x, N),
Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(N, ZZGreaterEqual(0)))))

## Topics using this entry

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

2020-04-08 16:14:44.404316 UTC