Sum of log squared terms?

Hi all,

I have a summation series which goes like this,

S = [log(1)]^2 + [log(2)]^2 + [log(3)]^2 + ....... + [log(n)]^2

Since each term is square of the logarithm of a value, I think there are no general tricks which can be used to solve this.

But is there any way to approximate the value of this summation?

The problem I am facing here is that n is very very large and it is not possible (time-wise and memory-wise) for my program to evaluate every term. So I was hoping for some approximate solution in terms of 'n'.

Thanks,

yogo