gamma function

I'll be grateful if you help me with the bolded part:

There is a very interesting function Γ: [0,http://upload.wikimedia.org/math/e/2...6098982278.png) ->R called the gamma function.
It is defined as http://upload.wikimedia.org/math/b/4...575b7c7523.png It has the remarkable property that if xhttp://upload.wikimedia.org/math/7/b...e1a4c7cff0.png N,
then http://upload.wikimedia.org/math/4/a...d24a3c28e7.png . Check that this is true for x=1,2,3,4.

Notice that this function provides a way of extending factorials to numbers other
than integers. Since http://upload.wikimedia.org/math/4/a...d24a3c28e7.png for all xhttp://upload.wikimedia.org/math/7/b...e1a4c7cff0.png N, we have the formula n!=Γ(n+1).
But Γ can be evaluated at any number in [0, http://upload.wikimedia.org/math/e/2...6098982278.png), not just at integers, so we
have a formula for n! for any nhttp://upload.wikimedia.org/math/7/b...e1a4c7cff0.png[0,http://upload.wikimedia.org/math/e/2...6098982278.png). Extra credit: Compute pi!

Thank you in advance!