The factorial of a non-negataive integer n, designated n!, can be defined recursively as
0! = 1
n! = n(n 1)! for n > 0.
Intuitively, for a positive integer n, n! is the product of positive integers up to and including n.
Sometimes it's more useful to think of n! as the product of positive integers from n down to 1. That viewpoint, for example, makes clear the relationship
n! = n(n 1)!
Factorials are used in counting numbers of permutations and combinations.
The gamma function is defined for all real numbers, but outputs factorial values for non-negative integer input. Information about the gamma function can be found in advanced calculus texts.
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