Definition:Omega Constant

Definition
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.

The value of $\Omega$ is approximately:


 * $0 \cdotp 56714 \, 32904 \, 097838 \, 72999 \, 96866 \, 22 \ldots$

Also see

 * Omega Constant is Transcendental