Definition:Lambert W Function

Definition
Let $f: \C \to \C$ be a complex function where:
 * $f \left({W}\right) := W e^W$

where $e$ denotes Euler's number.

The Lambert W function, denoted $W \left({z}\right)$, is the inverse of $f$, considered as a multifunction.

Graph

 * WRealBranches.png

Also known as
The Lambert W function is also called:
 * Lambert-W function
 * Lambert W-function
 * Lambert's W function
 * The $\Omega$ (omega) function
 * The Product Log function