Fungrim entry: a172c7

W_{-1}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)

Assumptions:

x \in \left(0, -\frac{1}{e}\right]

TeX:

W_{-1}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)

x \in \left(0, -\frac{1}{e}\right]

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W_{k}\!\left(z\right)$	Lambert W-function
`Log`	$\log\!\left(z\right)$	Natural logarithm
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`ConstE`	$e$	The constant e (2.718...)

Source code for this entry:

Entry(ID("a172c7"),
    Formula(Equal(LambertW(-1, Mul(x, Log(x))), Log(x))),
    Variables(x),
    Assumptions(Element(x, OpenClosedInterval(0, Neg(Div(1, ConstE))))))

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