**Stirling's approximation**

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## Stirling's approximation for factorials

Factorials can be approximated for large values of n using the
Sterling 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.

(stirling.xls)

© Bart J. Van Zeghbroeck, 1997