Stirling's approximation

Metadata
aliases: [Stirling's formula]
shorthands: {}
created: 2022-03-21 13:02:32
modified: 2022-03-21 13:05:59

The following approximation is true for factorials:

When .

Or with the more precise version:

Comment: the factorial is exchangeable with the gamma function.

Simple derivation

Since :

This sum can be approximated by the integral: