Re: Finding a sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg127387] Re: Finding a sum*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>*Date*: Fri, 20 Jul 2012 23:42:00 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <jub30p$eiv$1@smc.vnet.net>

On 20 Jul., 09:57, Hugh Goyder <h.g.d.goy... at cranfield.ac.uk> wrote: > 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}] > > The closed form is oo (the series are divergent) Regards, Wolfgang