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Fungrim entry: a172c7

W1 ⁣(xlog ⁣(x))=log ⁣(x)W_{-1}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)
Assumptions:x(0,1e]x \in \left(0, -\frac{1}{e}\right]
TeX:
W_{-1}\!\left(x \log\!\left(x\right)\right) = \log\!\left(x\right)

x \in \left(0, -\frac{1}{e}\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
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
ConstEee The constant e (2.718...)
Source code for this entry:
Entry(ID("a172c7"),
    Formula(Equal(LambertW(-1, Mul(x, Log(x))), Log(x))),
    Variables(x),
    Assumptions(Element(x, OpenClosedInterval(0, Neg(Div(1, ConstE))))))

Topics using this entry

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