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Fungrim entry: 30bd5b

W0 ⁣(xlog(x))=log(x)W_{0}\!\left(x \log(x)\right) = \log(x)
Assumptions:x[1e,)x \in \left[\frac{1}{e}, \infty\right)
TeX:
W_{0}\!\left(x \log(x)\right) = \log(x)

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(z) 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(Div(1, ConstE), Infinity))))

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2020-01-31 18:09:28.494564 UTC