Fungrim entry: a34260

W'_{0}\!\left(x\right) \lt \frac{2}{\sqrt{1 + e x}}

Assumptions:

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

TeX:

W'_{0}\!\left(x\right) \lt \frac{2}{\sqrt{1 + e x}}

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

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W_{k}\!\left(z\right)$	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
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("a34260"),
    Formula(Less(LambertW(0, x, 1), Div(2, Sqrt(Add(1, Mul(ConstE, x)))))),
    Variables(x),
    Assumptions(Element(x, OpenInterval(Neg(Exp(-1)), Infinity))))

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.

2019-06-18 07:49:59.356594 UTC