Fungrim entry: efebb8

\operatorname{atan}\!\left(x\right) \le {\left(\frac{\pi}{2}\right)}^{2} \frac{x}{1 + \frac{\pi}{2} x}

Assumptions:

x \in \left[0, \infty\right)

TeX:

\operatorname{atan}\!\left(x\right) \le {\left(\frac{\pi}{2}\right)}^{2} \frac{x}{1 + \frac{\pi}{2} x}

x \in \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`Pow`	${a}^{b}$	Power
`ConstPi`	$\pi$	The constant pi (3.14...)
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("efebb8"),
    Formula(LessEqual(Atan(x), Mul(Pow(Div(ConstPi, 2), 2), Div(x, Add(1, Mul(Div(ConstPi, 2), x)))))),
    Variables(x),
    Assumptions(Element(x, ClosedOpenInterval(0, Infinity))))

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.

2019-06-18 07:49:59.356594 UTC