Omega function

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

$\mathrm{\Omega }$ (big omega) may refer to:

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

$\omega$ (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 $n$.