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MATHEMATICA, need help with a triple sum

  1. Apr 6, 2012 #1
    I'm having trouble solving this summation and was wondering if anyone could put me on the right track. Here's the problem below, i've also attached a pdf of it.

    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?
     

    Attached Files:

  2. jcsd
  3. Apr 7, 2012 #2
    Sometimes something like this will give you a result
    Limit[Sum[((-1)^((m-1)/2))*(m/(n^2+l^2+m^2)), {l,1,i, 2}, {m,1,i,2}, {n,1,i,2}], i -> Infinity]
    but you need to carefully consider whether that is a valid change to your problem.
     
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