NIST

Stirling's approximation

(definition)

Definition: For large values of n, n! ≈ (n/e)n √(2nπ).

See also factorial, gamma function.

Note: This approximation is taken directly from Stirling's formula.

Author: PEB

More information

Peter Luschny lists and evaluates many approximation formulas for n!. See Eric W. Weisstein, Stirling's Approximation for a derivation and other approximations. A slightly different approximation and relative errors from Bart j. Van Zeghbroeck's book.


Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 4 May 2009.
HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:
Paul E. Black, "Stirling's approximation", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 4 May 2009. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/stirlingsApproximation.html