In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for large factorials. It is named after James Stirling.
The formula as typically used in applications is
The next term in the O(ln(n)) is (1/2)ln(2πn); a more precise variant of the formula is therefore
Sometimes, bounds for n! rather than asymptotics are required: one has, for all
so for all n ≥ 1 the ratio is always e.g. between 2.5 and 2.8.
Read more about Stirling's Approximation: Derivation, Speed of Convergence and Error Estimates, Stirling's Formula For The Gamma Function, A Convergent Version of Stirling's Formula, Versions Suitable For Calculators, History
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