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>.
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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 $n!=n \cdot (n-1) \cdots 2 \cdot 1$ 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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