Forumula for calculating $1\cdot 2\cdot3\cdot4\cdot5\cdot\ldots\cdot n$

Question

I'm looking for a formula to calculate the (product?) of an arithmetic series. Something like this:

$$\frac{n(a_1+a_n)}{2}$$

which is used to get the sum of the series, expect instead of all the elements added togethor, it would give all of the elements multiplied by each other.

Is there a formula for this? I've looked on the internet, but I don't know a lot of math terms so I don't know what to search.

Answer 1

This is the factorial function, $n\mapsto n!$. There is no neat formula for it as you might find for the sum, but there is Stirling's approximation $$n!\sim{n^ne^{-n}\over\sqrt{2\pi n}}.$$

Answer 2

This seem to be a decent formula, found on a page about the gamma function.

ref: http://www.sosmath.com/calculus/improper/gamma/gamma.html