I'll be grateful if you help me with the bolded part:
There is a very interesting function Γ: [0,) ->R called the gamma function.
It is defined as It has the remarkable property that if x N,
then . 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 for all x N, we have the formula n!=Γ(n+1).
But Γ can be evaluated at any number in [0, ), not just at integers, so we
have a formula for n! for any n[0,). Extra credit: Compute pi!
Thank you in advance!