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Fungrim entry: 8654a3

W0 ⁣(xex)=xW_{0}\!\left(x {e}^{x}\right) = x
Assumptions:x[1,)x \in \left[-1, \infty\right)
TeX:
W_{0}\!\left(x {e}^{x}\right) = x

x \in \left[-1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
Expez{e}^{z} Exponential function
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("8654a3"),
    Formula(Equal(LambertW(0, Mul(x, Exp(x))), x)),
    Variables(x),
    Assumptions(Element(x, ClosedOpenInterval(-1, 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