# Fungrim entry: 88168b

$W_{k}\!\left(z\right) \exp\!\left(W_{k}\!\left(z\right)\right) = z$
Assumptions:$\left(k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}\right) \;\mathbin{\operatorname{or}}\; \left(k = 0 \;\mathbin{\operatorname{and}}\; z = 0\right)$
TeX:
W_{k}\!\left(z\right) \exp\!\left(W_{k}\!\left(z\right)\right) = z

\left(k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}\right) \;\mathbin{\operatorname{or}}\; \left(k = 0 \;\mathbin{\operatorname{and}}\; z = 0\right)
Definitions:
Fungrim symbol Notation Short description
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
Exp${e}^{z}$ Exponential function
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("88168b"),
Formula(Equal(Mul(LambertW(k, z), Exp(LambertW(k, z))), z)),
Variables(k, z),
Assumptions(Or(And(Element(k, ZZ), Element(z, SetMinus(CC, Set(0)))), And(Equal(k, 0), Equal(z, 0)))))

## Topics using this entry

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

2020-04-08 16:14:44.404316 UTC