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

Lambert W-function