\begin{definition}[Definition:Omega Constant]
The '''omega constant''' $\Omega$ is the constant as the value of the principal branch of the Lambert W function at $1$:
:$\Omega \, e^ \Omega = 1$
That is, it is the root of the equation:
:$x e^x = 1$
where $e$ denotes Euler's number.
\end{definition}