Fungrim entry: 9be916

\left|W'_{-1}\!\left(x\right)\right| < \frac{2}{\sqrt{1 + e x}} + \frac{2}{\left|x\right|}

Assumptions:

x \in \left(-{e}^{-1}, 0\right)

TeX:

\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)

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`Sqrt`	$\sqrt{z}$	Principal square root
`ConstE`	$e$	The constant e (2.718...)
`OpenInterval`	$\left(a, b\right)$	Open interval
`Exp`	${e}^{z}$	Exponential function

Source code for this entry:

Entry(ID("9be916"),
    Formula(Less(Abs(LambertW(x, -1, 1)), Add(Div(2, Sqrt(Add(1, Mul(ConstE, x)))), Div(2, Abs(x))))),
    Variables(x),
    Assumptions(Element(x, OpenInterval(Neg(Exp(-1)), 0))))

Topics using this entry

Lambert W-function

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