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.