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Fungrim entry: ed7dac

W1 ⁣(xex)=xW_{-1}\!\left(x {e}^{x}\right) = x
Assumptions:x(,1]x \in \left(-\infty, -1\right]
TeX:
W_{-1}\!\left(x {e}^{x}\right) = x

x \in \left(-\infty, -1\right]
Definitions:
Fungrim symbol Notation Short description
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
Expez{e}^{z} Exponential function
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("ed7dac"),
    Formula(Equal(LambertW(-1, Mul(x, Exp(x))), x)),
    Variables(x),
    Assumptions(Element(x, OpenClosedInterval(Neg(Infinity), -1))))

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

2019-09-15 14:14:26.267625 UTC