Omega function

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

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

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

${\displaystyle \omega }$ (omega) may refer to:

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