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Fungrim entry: 6191cd

BranchCuts ⁣(Wk ⁣(z),z,C)={(,0]}\operatorname{BranchCuts}\!\left(W_{k}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, 0\right]\right\}
Assumptions:kZ{1,0,1}k \in \mathbb{Z} \setminus \left\{-1, 0, 1\right\}
TeX:
\operatorname{BranchCuts}\!\left(W_{k}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, 0\right]\right\}

k \in \mathbb{Z} \setminus \left\{-1, 0, 1\right\}
Definitions:
Fungrim symbol Notation Short description
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("6191cd"),
    Formula(Equal(BranchCuts(LambertW(k, z), z, CC), Set(OpenClosedInterval(Neg(Infinity), 0)))),
    Variables(k),
    Assumptions(Element(k, SetMinus(ZZ, Set(-1, 0, 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