For any non-negative integer n, the factorialMathworldPlanetmath of n, denoted n!, can be defined by


where for n=0 the empty product is taken to be 1.

Alternatively, the factorial can be defined recursively by 0!=1 and n!=n(n-1)! for n>0.

n! is equal to the number of permutationsMathworldPlanetmath of n distinct objects. For example, there are 5! ways to arrange the five letters A, B, C, D and E into a word.

For every non-negative integer n we have


where Γ is Euler’s gamma functionDlmfDlmfMathworldPlanetmath. In this way the notion of factorial can be generalized to all complex (http://planetmath.org/Complex) values except the negative integers.

Title factorial
Canonical name Factorial
Date of creation 2013-03-22 11:53:58
Last modified on 2013-03-22 11:53:58
Owner yark (2760)
Last modified by yark (2760)
Numerical id 22
Author yark (2760)
Entry type Definition
Classification msc 05A10
Classification msc 11B65
Classification msc 92-01
Classification msc 92B05
Synonym factorial function
Related topic BinomialCoefficient
Related topic ExponentialFactorial