Factorial

Revision as of 14:52, 23 June 2006 by ComplexZeta (talk | contribs)

The factorial is an important function in combinatorics and analysis, used to determine the number of ways to arrange objects.

Definition

The factorial is defined for positive integers as $n!=n \cdot (n-1) \cdots 2 \cdot 1$ Alternatively, a recursive definition for the factorial is: $n!=n \cdot (n-1)!$.

Additional Information

By convention, $0!$ is given the value $1$.

The gamma function is a generalization of the factorial to values other than nonnegative integers.

Uses

The factorial is used in the definitions of combinations and permutations, as $n!$ is the number of ways to order $n$ distinct objects.

Examples

See also

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