Fungrim entry: d04a5b

\operatorname{atan}\!\left(x\right) \le \frac{\pi}{2} \tanh\!\left(x\right)

Assumptions:

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

TeX:

\operatorname{atan}\!\left(x\right) \le \frac{\pi}{2} \tanh\!\left(x\right)

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

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`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("d04a5b"),
    Formula(LessEqual(Atan(x), Mul(Div(ConstPi, 2), Tanh(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