Stirling's approximation

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Stirling's approximation for factorials

Factorials can be approximated for large values of n using the Stirling approximation which is given by:

This equation yields n! with a relative error smaller than 1/4 % for all integer values of n and with a relative error smaller than 3.5 x 10-7 for n > 20.

The exact and approximate values for n = 1, 2, ... 10 and the relative error are provided in the table below.

© Bart J. Van Zeghbroeck, 1997