# Fungrim entry: 276d78

$\operatorname{BranchCuts}\!\left(W_{k}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, -{e}^{-1}\right], \left[-{e}^{-1}, 0\right], \left(-\infty, 0\right]\right\}$
Assumptions:$k \in \left\{-1, 1\right\}$
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
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
CC$\mathbb{C}$ Complex numbers
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
Exp${e}^{z}$ Exponential function
ClosedInterval$\left[a, b\right]$ 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))))

## 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