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

Lambert W-function