# Difference between revisions of "Factorial"

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=== Definition === | === Definition === | ||

− | The factorial is defined for positive integers as <math>n!=n \cdot (n-1) \cdots 2 \cdot 1</math> Alternatively, a recursive definition for the factorial is: <math>n!=n \cdot (n-1)!</math>. | + | The factorial is defined for positive integers as <math>n!=n \cdot (n-1) \cdots 2 \cdot 1</math> Alternatively, a [[recursion|recursive definition]] for the factorial is: <math>n!=n \cdot (n-1)!</math>. |

=== Additional Information === | === Additional Information === |

## Revision as of 15:36, 23 June 2006

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 Alternatively, a recursive definition for the factorial is: .

### Additional Information

By convention, is given the value .

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 is the number of ways to order distinct objects.