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I'm physicist, in my work on BEC i have encountered infinite sum, which i expect could be expressed as analytic function. I ask for your help, any hints will be very helpful. Best regards.

$\sum_{kl}^{\infty}\sum_{ij}^{\infty}\frac{1}{A\exp(ak+bl+2ci+d)+1}\frac{1}{A\exp(ak+bl+c(2j+1)+d)+1} \frac{1}{4^{i+j}}\frac{(2i)!(2j+1)!}{(i!)^{2}(j!)^{2}(2j+1-2i)^{2}}$

A, a, b, c, d are positive constants.

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What do you mean by $\sum_{kl}^\infty \sum_{ij}^\infty$? –  Robert Israel Mar 18 '12 at 19:01
In any case, it's unlikely that a sum like this could have a closed form. Even $\sum_{i=0}^\infty 1/(\exp(i)+1)$ doesn't. –  Robert Israel Mar 18 '12 at 19:14
Thanks for interest. These are sums from $k=0$ to $k=\infty$, from $l=0$ to $l=\infty$ and so on. –  weiss Mar 18 '12 at 19:15
So, what is the question? –  Gerry Myerson Mar 18 '12 at 22:24
You really have to be more precise. You have an infinite sum, which is a number. That number of course can be expressed as an "analytic function", for example the constant function equal to that number. Maybe you can show an example of a similar calculation where you can obtain an "analytic function" so that we have an idea of what it is you want? –  Vladimir Dotsenko Mar 19 '12 at 8:37

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