Big Omega function

The notation $\Omega ({\text{ }})\,\!$ has at least three meanings in mathematics:

$f\in \Omega (g)\,\!$ means that the function $f\,\!$ dominates $g\,\!$ in some limit, see Big O notation. In this context $\Omega$ is referred to as a lower bound.
$\Omega (n)\,\!$ is the total number of prime factors of $n\,\!$ , counting prime factors with multiplicity
$\Omega (x)\,\!$ may refer to the Omega function, the inverse of $y=x\cdot e^{{x}}\,\!$ , also known as the Lambert W function denoted $W(x)\,\!$ .
- $\omega (x)\,\!$ , related to the Lambert W Function, is called the Wright Omega Function

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