Definition: For large values of n, (n/e)n √(2nπ) < n! < (n/e)n(1 + 1/(12n-1)) √(2nπ).
See also Stirling's approximation, factorial, gamma function.
Note: After CRC Standard Mathematical Tables, Fourteenth Edition, Samuel M. Selby, ed., page 433, 1965.
Peter Luschny lists and evaluates many approximation formulas for n!. See Eric W. Weisstein, Stirling's Approximation for a derivation and other approximations.
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 10 November 2008.
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Cite this as:
Paul E. Black, "Stirling's formula", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 10 November 2008. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/stirlingsFormula.html