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The factorial $ n!$ is defined as the product of the first $ n$ positive integers, that is

$\displaystyle n! = 1\cdot 2 \cdots n

Maintaining consistency with the definition of the empty product, $ 0!$ is defined to have value $ 1$.

The number $ n!$ corresponds to the number of possibilities to arrange n distinct objects.

For large $ n$, the asymptotic behavior of $ n!$ can be approximated by Stirling's formula:

$\displaystyle n! = \sqrt{2\pi n}\left(\frac{n}{e}\right)^n(1+{\cal O}(1/n))\,.

(Authors: Höllig/Hörner/Abele)

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  automatically generated 6/11/2007