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Fungrim entry: 30bd5b

W0 ⁣(xlog ⁣(x))=log ⁣(x)W_{0}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)
Assumptions:x[1e,)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
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
ConstEee 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))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-16 21:17:18.797188 UTC