Difference between revisions of "Factorial"

 
(Added basic information about factorials)
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See [[Combinatorics]]
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=== Definition ===
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An important concept in [[combinatorics]], 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>.
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=== Additional Information ===
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By convention, <math>0!</math> is given the value <math>1</math>.
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The [[gamma function]] is a generalization of the factorial to values other than positive integers.
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=== Uses ===
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The factorial is used in the definitions of [[combinations]] and [[permutations]], as <math>n!</math> is the number of ways to order <math>n</math> distinct objects.

Revision as of 12:12, 18 June 2006

Definition

An important concept in combinatorics, 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 positive 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.

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