# Big Omega function

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