Proof of Stirling formula

0. introduction

Stirling's formula （Stirling’s approximation） It's one for taking n Of Factorial Of Approximate value Mathematical formula of . Generally speaking , The computational complexity of factorial is linear . When it comes to something very big n Factorial time , The complexity of common methods is unacceptable . Stirling formula can reduce the complexity of solving factorial to logarithmic order . and , Even in n When I was very young , The value of Stirling formula is very accurate .

1. prove

2. utilize Wallis The formula ,

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About the step of integral expansion and contraction