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

There is a very interesting functionΓ: [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).

ButΓcan 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!