# Getting the square of implicit summation terms

I was wondering whether it is possible to use a product or summation (or other simplified way) to compute a formula of the type $e^{u^2}+e^{v^2}+e^{(u+v)^2}$. It is quite easy to obtain $e^{u}+e^{v}+e^{u+v}$ by using $\prod_x (1+e^x)$, where $x\in \{v,u\}$ in this case. I'm not sure if this is also possible in some way when the square is involved. Of course I can easily compute this for a couple of variables but I'm looking for something that scales to a larger number of them. If someone is sure that there is no elegant solution for this I'd also like to know of course.

 $e^{u^2}+e^{v^2}+e^{(u+v)^2}$ - you're already adding stuff up here; what more do you need? – J. M. Sep 28 '11 at 9:59 What did you get, when you easily compute this for a couple of variables? – draks ... Apr 5 '12 at 18:35