# Factorial function

1. Apr 12, 2008

### Pacopag

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

2. Apr 12, 2008

### rock.freak667

In general, n! is only for integers.

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

3. Apr 12, 2008

### HallsofIvy

Staff Emeritus
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.