Big Omega function

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The notation \Omega (\text{ })\,\! has at least three meanings in mathematics:

  • f = \Omega (g)\,\! means that the function f\,\! dominates g\,\! in some limit, see Big O notation. In this context \Omega is referred to as a lower bound.
  • \Omega(n)\,\! is the total number of prime factors of n\,\!, counting prime factors with multiplicity
  • \Omega(x)\,\! may refer to the Omega function, the inverse of y = x\cdot e^{x} \,\!, also known as the Lambert W function denoted W(x)\,\!.

A function f(n) is Omega (g) -often written "in the complexity class of Omega(g(n))" if there are values c and n0 such that f(n) >= c g(n) for all n>n0

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