# Omega function

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In mathematics, **omega function** refers to a function using the Greek letter [omega](/source/Omega), written ω or Ω.

\Omega (big omega) may refer to:

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

\omega (omega) may refer to:

- The [Wright omega function](/source/Wright_omega_function) \omega(x)\,\!, related to the Lambert W Function
- The [Pearson–Cunningham function](/source/Pearson%E2%80%93Cunningham_function) \omega_{m,n}(x)
- The [prime omega function](/source/Prime_omega_function) \omega(n)\,\!, giving the number of distinct prime factors of n\,\!.

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Adapted from the Wikipedia article [Omega function](https://en.wikipedia.org/wiki/Omega_function) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Omega_function?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.