# Fungrim entry: 2caf78

$\operatorname{HolomorphicDomain}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, 0\right]$
Assumptions:$k \in \mathbb{Z} \setminus \left\{0\right\}$
TeX:
\operatorname{HolomorphicDomain}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, 0\right]

k \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
CC$\mathbb{C}$ Complex numbers
UnsignedInfinity${\tilde \infty}$ Unsigned infinity
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("2caf78"),
Formula(Equal(HolomorphicDomain(LambertW(k, z), z, Union(CC, Set(UnsignedInfinity))), SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))),
Variables(k),
Assumptions(Element(k, SetMinus(ZZ, Set(0)))))

## Topics using this entry

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

2019-09-16 21:17:18.797188 UTC