Definition:Lambert W Function

Definition
Let $e^z: \C \to \C$ be the complex exponential.

Then $W\left({z}\right)$ is defined to be the multifunction that satisfies:


 * $W\left({z}\right)e^{W\left({z}\right)}=z$

Real Valued Principal Branch

 * WRealBranches.png

Complex Valued Principal Branch

 * W Re.png


 * W Im.png


 * W mod.png


 * W Arg.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