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Fungrim entry: efebb8

atan ⁣(x)(π2)2x1+π2x\operatorname{atan}\!\left(x\right) \le {\left(\frac{\pi}{2}\right)}^{2} \frac{x}{1 + \frac{\pi}{2} x}
Assumptions:x[0,)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
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
ClosedOpenInterval[a,b)\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))))

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

2019-09-22 15:43:45.410764 UTC