Factorial
From Encyclopedia of Mathematics
The function defined on the set of non-negative integers with value at 
equal to the product of the natural numbers from 1 to 
, that is, to 
; it is denoted by 
(by definition, 
). For large 
an approximate expression for the factorial is given by the Stirling formula. The factorial is equal to the number of permutations of 
elements. The more general expression
 |
is also called a factorial, where 
is a complex number, 
is a natural number, and 
. See also Gamma-function.
Comments
Because 
equals the number of permutations of 
elements, the factorial is extensively used in combinatorics, probability theory, mathematical statistics, etc. Cf. Combinatorial analysis; Combination; Binomial coefficients.
How to Cite This Entry:
Factorial. BSE-3 (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Factorial&oldid=18764
Factorial. BSE-3 (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Factorial&oldid=18764
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098