Fungrim entry: 2caf78

W_{k}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \left(-\infty, 0\right]

Assumptions:

k \in \mathbb{Z} \setminus \left\{0\right\}

TeX:

W_{k}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \left(-\infty, 0\right]

k \in \mathbb{Z} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`IsHolomorphic`	$f(z) \text{ is holomorphic at } z = c$	Holomorphic predicate
`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("2caf78"),
    Formula(IsHolomorphic(LambertW(z, k), ForElement(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))),
    Variables(k),
    Assumptions(Element(k, SetMinus(ZZ, Set(0)))))

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