Factorial Function: Does it Hold for Non-Integer N?

[Pacopag]

Homework Statement

I was just wondering if
$$n!=n(n-1)!$$
is completely general. Does it hold even for non-integer n?

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

In general, n! is only for integers.

(But it is possible to compute nCr for n being negative or a non-integer.)

 

[HallsofIvy]

How would you define n! for non-integer in order to have it hold?

The gamma functions, $\Gamma(z)= \int_0^\infty t^{z-1} e^{-t}dt$ has the property that $\Gamma(z)= (z-1)!$ for z a positive integer, and is defined for all z except negative integers.