PlanetMath: factorial

(more info)

Math for the people, by the people.

Main Menu

factorial

(Definition)

For any non-negative integer , the factorial of , denoted , can be defined by

$\displaystyle n!=\prod_{r=1}^n r$

where for

the empty product is taken to be

Alternatively, the factorial can be defined recursively by and for .

is equal to the number of permutations of distinct objects. For example, there are ways to arrange the five letters A, B, C, D and E into a word.

For every non-negative integer we have

$\displaystyle \Gamma(n+1) = n!$

where $\Gamma$ is Euler's gamma function. In this way the notion of factorial can be generalized to all complex values except the negative integers.

"factorial" is owned by yark. [ full author list (2) | owner history (1) ]

(view preamble)

Other names:

factorial function

Attachments:: the prime power dividing a factorial (Theorem) by Thomas Heye
factorial prime (Definition) by PrimeFan
recursive algorithm for factorial function (Algorithm) by PrimeFan
factorion (Definition) by Mravinci

Log in to rate this entry.
(view current ratings)

Cross-references: negative, Euler's gamma function, objects, permutations, empty product, integer
There are 31 references to this entry.

This is version 17 of factorial, born on 2001-10-26, modified 2006-10-09.
Object id is 516, canonical name is Factorial.
Accessed 16589 times total.

Classification:

AMS MSC:	05A10 (Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions)
	11B65 (Number theory :: Sequences and sets :: Binomial coefficients; factorials; $q$-identities)

Pending Errata and Addenda

None.[ View all 5 ]

Discussion

forum policy

No messages.

Interact