Stirling's approximation

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In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of n {\displaystyle n} . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: ln ⁡ n ! = n ln ⁡ n − n + O ( ln ⁡ n ) , {\displaystyle \ln n!=n\ln n-n+O(\ln n),} where the big O notation means that, for all sufficiently large values of n {\displaystyle n} , the difference between ln ⁡ n ! {\displaystyle \ln n!} and...

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