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# Fungrim entry: 314807

$\mathop{\operatorname{solution*}\,}\limits_{w \in \left[-1, \infty\right)} \left[w {e}^{w} = x\right] = W_{0}\!\left(x\right)$
Assumptions:$x \in \left[-\frac{1}{e}, \infty\right)$
TeX:
\mathop{\operatorname{solution*}\,}\limits_{w \in \left[-1, \infty\right)} \left[w {e}^{w} = x\right] = W_{0}\!\left(x\right)

x \in \left[-\frac{1}{e}, \infty\right)
Definitions:
Fungrim symbol Notation Short description
UniqueSolution$\mathop{\operatorname{solution*}\,}\limits_{x \in S} Q(x)$ Unique solution
Exp${e}^{z}$ Exponential function
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
ConstE$e$ The constant e (2.718...)
Source code for this entry:
Entry(ID("314807"),
Formula(Equal(UniqueSolution(Brackets(Equal(Mul(w, Exp(w)), x)), ForElement(w, ClosedOpenInterval(-1, Infinity))), LambertW(0, x))),
Variables(x),
Assumptions(Element(x, ClosedOpenInterval(Neg(Div(1, ConstE)), Infinity))))

## Topics using this entry

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

2020-01-31 18:09:28.494564 UTC