Finding a sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg127373] Finding a sum*From*: Hugh Goyder <h.g.d.goyder at cranfield.ac.uk>*Date*: Fri, 20 Jul 2012 03:53:33 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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}]