Fungrim entry: e6e7a2

\operatorname{BranchPoints}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{0, {\tilde \infty}\right\}

Assumptions:

k \in \mathbb{Z} \setminus \left\{-1, 0, 1\right\}

TeX:

\operatorname{BranchPoints}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{0, {\tilde \infty}\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
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("e6e7a2"),
    Formula(Equal(BranchPoints(LambertW(z, k), z, Union(CC, Set(UnsignedInfinity))), Set(0, UnsignedInfinity))),
    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