CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Comparison of Stirling's approximation with the factorial In mathematics , Stirling's approximation (or Stirling's formula ) is an approximation for factorials . It is a very powerful approximation, leading to accurate results even for small values of n . It is named after James Stirling , though it was first stated by Abraham de Moivre . [ 1 ] [ 2 ] [ 3 ] The formula as typically used in applications is (in big O notation ). The next term in the O (ln( n )) is (1/2)ln(2π n ); a more precise variant of the formula is therefore As an asymptotic formula , Stirling's approximation has the property that the ratio approaches 1 as n grows to infinity. 1 Derivation 2 An alternative derivation 3 Speed of convergence and error estimates 4 Stirling's formula for the gamma ...