factorial
For any non-negative integer , the factorial of , denoted , can be defined by
where for the empty product is taken to be .
Alternatively, the factorial can be defined recursively by and for .
is equal to the number of permutations of distinct objects. For example, there are ways to arrange the five letters A, B, C, D and E into a word.
For every non-negative integer we have
where is Euler’s gamma function. 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 |