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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)
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  • 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



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