Omega function

In mathematics, omega function refers to a function using the Greek letter omega, written ω or Ω.

$\Omega$ (big omega) may refer to:

• The lower bound in Big O notation, $f\in \Omega (g)\,\!$, meaning that the function $f\,\!$ dominates $g\,\!$ in some limit
• The prime omega function $\Omega (n)\,\!$, giving the total number of prime factors of $n\,\!$, counting them with their multiplicity.
• The Lambert W function $\Omega (x)\,\!$, the inverse of $y=x\cdot e^{x}\,\!$, also denoted $W(x)\,\!$.

$\omega$ (omega) may refer to:

• The Wright Omega Function $\omega (x)\,\!$, related to the Lambert W Function
• The Pearson–Cunningham function $\omega _{m,n}(x)$
• The prime omega function $\omega (n)\,\!$, giving the number of distinct prime factors of $n\,\!$.