# A formula of the product of the first n integers?

1. Sep 18, 2006

### quasar987

I'm sure it exists, and it'd help me to have it. Thx!

2. Sep 18, 2006

### AKG

n!

.......................

3. Sep 18, 2006

### quasar987

No no, like there's n(n+1)/2 for the sum of the first n integers. Is there an equivalent formula for the product?

4. Sep 18, 2006

### d_leet

I want to say no since if there was we would probably use that instead of n! everywhere, but there's stirling's approximation to n!.

Last edited: Sep 18, 2006
5. Sep 18, 2006

### quasar987

You're probably right.

6. Sep 19, 2006

### CRGreathouse

Stirling's formula gives a good approximation. I prefer to use Gosper's reformulation of same.

7. Sep 19, 2006

### Parlyne

Well, there's always the integral form of the factorial function; although I doubt it's what you're looking for:

$$n! = \Gamma(n+1) = \int_0^{\infty} e^{-t} t^n dt$$

8. Sep 19, 2006

### Robokapp

it's n(n+1)/2 if you start at 1 and n(n-1)/2 if you start at zero if I recall...

9. Sep 19, 2006

### CRGreathouse

I think you mean n and n-1, respectively, if you're talking about sums. Obviously adding in 0 has no effect.