Stirling's Approximation

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

often written

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 ApproximationDerivation, 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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