# Fungrim entry: d7136f

$\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[w {e}^{w} = z\right] = \left\{ W_{k}\!\left(z\right) : k \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(z \ne 0 \,\mathbin{\operatorname{or}}\, k = 0\right) \right\}$
Assumptions:$z \in \mathbb{C}$
TeX:
\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[w {e}^{w} = z\right] = \left\{ W_{k}\!\left(z\right) : k \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, \left(z \ne 0 \,\mathbin{\operatorname{or}}\, k = 0\right) \right\}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Solutions$\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right)$ Solution set
Exp${e}^{z}$ Exponential function
CC$\mathbb{C}$ Complex numbers
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("d7136f"),
Formula(Equal(Solutions(Brackets(Equal(Mul(w, Exp(w)), z)), w, Element(w, CC)), SetBuilder(LambertW(k, z), k, And(Element(k, ZZ), Or(Unequal(z, 0), Equal(k, 0)))))),
Variables(z),
Assumptions(Element(z, CC)))

## 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