Fungrim entry: 6191cd

\operatorname{BranchCuts}\!\left(W_{k}\!\left(z\right), z, \mathbb{C}\right) = \left\{\left(-\infty, 0\right]\right\}

Assumptions:

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
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("6191cd"),
    Formula(Equal(BranchCuts(LambertW(z, k), z, CC), Set(OpenClosedInterval(Neg(Infinity), 0)))),
    Variables(k),
    Assumptions(Element(k, SetMinus(ZZ, Set(-1, 0, 1)))))

Topics using this entry

Lambert W-function

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

2021-03-15 19:12:00.328586 UTC