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When can interchange sum and integral

  1. Dec 24, 2012 #1
    Why in the attached picture is it legal to interchange the sum and integral? Is it just because n is not dependent on t? note: (c1)n is just a function of n
     

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  2. jcsd
  3. Dec 24, 2012 #2

    micromass

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    You would have to apply something like the monotone or dominated convergence theorem to prove that it is valid in this case.
     
  4. Dec 26, 2012 #3
    The reason you can interchange is not because the variables are independent but because the operations are; that is, the integration and the summation.
     
    Last edited: Dec 26, 2012
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