factorial

(definition)

Definition: The factorial of an integer n ≥ 0, written n!, is n × n-1 × ... × 2 × 1. In particular, 0! = 1.

Generalization (I am a kind of ...)
gamma function.

Specialization (... is a kind of me.)
Stirling's approximation.

Aggregate parent (I am a part of or used in ...)
permutation, combination.

Note: For instance 5! = 120. Factorial is often used as a (poor) example of recursion, since n! = n × (n-1)! for n > 1, however a simple loop is usually faster and just as clear.

Why is 0! = 1? Using the gamma function definition, 0! = Γ(0+1) = ∫ ₀^∞ e^-xx^1-1dx = ∫ ₀^∞ e^-xdx = 1.

Author: PEB

Implementation

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

Entry modified 28 July 2008.
HTML page formatted Tue Dec 6 16:16:32 2011.

Cite this as:
Paul E. Black, "factorial", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 28 July 2008. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/factorial.html