Fungrim entry: 30bd5b

W_{0}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)

Assumptions:

x \in \left[-\frac{1}{e}, \infty\right)

TeX:

W_{0}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)

x \in \left[-\frac{1}{e}, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W_{k}\!\left(z\right)$	Lambert W-function
`Log`	$\log\!\left(z\right)$	Natural logarithm
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`ConstE`	$e$	The constant e (2.718...)
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("30bd5b"),
    Formula(Equal(LambertW(0, Mul(x, Log(x))), Log(x))),
    Variables(x),
    Assumptions(Element(x, ClosedOpenInterval(Neg(Div(1, ConstE)), 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