Stirling's Theorem

Stirling's Theorem

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

Being an asymptotic formula, Stirling's approximation has the property that

Bounds for the above ratio can be given: one has, for all n in N+,

Read more about Stirling's Theorem:  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, See Also

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