Asymptotic behavior of this function?

1. Aug 7, 2014

asmani

Hi

How to estimate the asymptotic behavior of this function?

$$f(x)=\sum_{k=1}^{x}\log(k)$$
I mean, a closed form function g(x) such that f(x)/g(x) tends to 1 as x goes to infinity.

2. Aug 7, 2014

pasmith

x is an integer, yes? Then $f(x) = \log(x!)$. The standard asymptotic approximation for the factorial function is Stirling's approximation.

3. Aug 7, 2014

asmani

Haha, exactly what I was looking for. Thanks!

4. Aug 8, 2014

micromass

Staff Emeritus