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.

Decimal Expansion

The decimal expansion of the omega constant $\Omega$ starts:

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

Also see

• Omega Constant is Transcendental

• Results about the omega constant can be found here.

Sources

• Weisstein, Eric W. "Omega Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OmegaConstant.html