# Difference between revisions of "Factorial"

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− | The '''factorial''' is an important | + | The '''factorial''' is an important function in [[combinatorics]] and [[analysis]], used to determine the number of ways to arrange objects. |

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

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By convention, <math>0!</math> is given the value <math>1</math>. | By convention, <math>0!</math> is given the value <math>1</math>. | ||

− | The [[gamma function]] is a generalization of the factorial to values other than | + | The [[gamma function]] is a generalization of the factorial to values other than nonnegative integers. |

=== Uses === | === Uses === |

## Revision as of 14:52, 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.