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Finding a sum

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  • Subject: [mg127373] Finding a sum
  • From: Hugh Goyder <h.g.d.goyder at>
  • Date: Fri, 20 Jul 2012 03:53:33 -0400 (EDT)
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I feel the sum below should have a closed form. Am I wrong? A direct attack does not work. However, by experimenting I can sum a row but I can't sum all the rows. Any ideas? Thanks.

Sum[1/(x + I y - (n + I m)), 
{n, -Infinity, Infinity}, {m, -Infinity,Infinity}]

Srow = 1/(x + I y) + 
  Sum[1/(x + I y - (n + I m)) + 1/(x + I y - (-n + I m)), 
{n, 1 , Infinity}]

Sum[Srow + (Srow /. m -> -m), {m, 1, Infinity}]

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