factorial (original) (raw)

(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-xx1-1dx = ∫ 0∞ e-xdx = 1.

Author: PEB

Implementation

Peter Luschny's fast factorial algorithms (Java and C#) including benchmarks and advice.

Go to theDictionary of Algorithms and Data Structures home page.

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

Entry modified 2 March 2015.
HTML page formatted Wed Oct 30 12:15:30 2024.

Cite this as:
Paul E. Black, "factorial", inDictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 2 March 2015. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/factorial.html