<mathematics> The mathematical function that takes a natural number, N,
and returns the product of N and all smaller positive integers. This is written
N! = N * (N-1) * (N-2) * ... * 1.
The factorial of zero is one because it is an empty product.
Factorial can be defined recursively as
0! = 1
N! = N * (N-1)! , N > 0
The gamma function is the equivalent for real numbers.
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