Omega function

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

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

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

$\backslash omega$ (omega) may refer to:

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

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