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Fungrim entry: 9be916

W1 ⁣(x)<21+ex+2x\left|W'_{-1}\!\left(x\right)\right| < \frac{2}{\sqrt{1 + e x}} + \frac{2}{\left|x\right|}
Assumptions:x(e1,0)x \in \left(-{e}^{-1}, 0\right)
\left|W'_{-1}\!\left(x\right)\right| < \frac{2}{\sqrt{1 + e x}} + \frac{2}{\left|x\right|}

x \in \left(-{e}^{-1}, 0\right)
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
Sqrtz\sqrt{z} Principal square root
ConstEee The constant e (2.718...)
OpenInterval(a,b)\left(a, b\right) Open interval
Expez{e}^{z} Exponential function
Source code for this entry:
    Formula(Less(Abs(LambertW(x, -1, 1)), Add(Div(2, Sqrt(Add(1, Mul(ConstE, x)))), Div(2, Abs(x))))),
    Assumptions(Element(x, OpenInterval(Neg(Exp(-1)), 0))))

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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