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Fungrim entry: 276d78

BranchCuts ⁣(Wk ⁣(z),z,C)={(,e1],[e1,0],(,0]}\operatorname{BranchCuts}\!\left(W_{k}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, -{e}^{-1}\right], \left[-{e}^{-1}, 0\right], \left(-\infty, 0\right]\right\}
Assumptions:k{1,1}k \in \left\{-1, 1\right\}
TeX:
\operatorname{BranchCuts}\!\left(W_{k}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, -{e}^{-1}\right], \left[-{e}^{-1}, 0\right], \left(-\infty, 0\right]\right\}

k \in \left\{-1, 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
Expez{e}^{z} Exponential function
ClosedInterval[a,b]\left[a, b\right] Closed interval
Source code for this entry:
Entry(ID("276d78"),
    Formula(Equal(BranchCuts(LambertW(k, z), z, CC), Set(OpenClosedInterval(Neg(Infinity), Neg(Exp(-1))), ClosedInterval(Neg(Exp(-1)), 0), OpenClosedInterval(Neg(Infinity), 0)))),
    Variables(k),
    Assumptions(Element(k, Set(-1, 1))))

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2019-09-16 21:17:18.797188 UTC