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This problem arose in finding a sum of expectations of Geometric RVs.

Any idea how to simplify the sum

\sum_{k=0}^{\frac{n}{2}-1}\frac{1}{(2n^2)^{c'}-(n^2+4k^2)^{c'}}

where c' is an integer. It would be good to obtain some digamma function from it.

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    Yes. ${}\qquad$2011-04-14

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