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MathGroup Archive 2012

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Re: complex triple sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125999] Re: complex triple sum
  • From: danl at wolfram.com
  • Date: Thu, 12 Apr 2012 02:34:42 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jlp379$16e$1@smc.vnet.net>

On Saturday, April 7, 2012 5:00:09 AM UTC-5, Greg wrote:
> I'm having trouble solving this summation and was wondering if anyone could put me on the right track. Here's the problem below.
> 
> Sum from 1 to infinity in steps of 2 for l, m, and n:((-1)^((m - 1)/2))*(m/(n^2 + l^2 + m^2)) 
> 
> I've tried using the built in sum functions
> 
> Sum[((-1)^((m - 1)/2))*(m/(n^2 + l^2 + m^2)),{l,1,Infinity,2},{m,1,Infinity,2},{n,1,Infinity,2}]
> 
> but mathematica continuously sums this and never reaches an approximation. Is there any function I'm missing or a way to simplify this?

In what sense do you want it summed? Classically, it is divergent. I do not know why Sum takes so long to unravel this though.

Daniel Lichtblau
Wolfram Research



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