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Notation for special summations

  1. Aug 5, 2008 #1
    Is there special notation for a function like this:



    If so, what would g(x_n) be?
  2. jcsd
  3. Aug 5, 2008 #2
    I forgot to add, a function like this:


    (the limit of each sum is another sum; fallowing the pattern in the above post of course)
  4. Aug 5, 2008 #3

    Ben Niehoff

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    For a small, finite number of indexes, sometimes I see the shorthand

    [tex]\sum_{i,j,k} f(x)[/tex]

    This usually occurs when all of the indexes run from 0 to the same limit N.

    If you have a variable number of indexes, then you can "index the indexes" as follows:

    [tex]S_n = \sum_{i_1 \dots i_n} f(x)[/tex]

    Oh, wait, I see you want each index to run up to the previous index. For a small number of indexes, you can do

    [tex]S_3 = \sum^N_{i > j > k} a_{ijk}(x)[/tex]

    And in general, you could probably write

    [tex]S_n = \sum^N_{i_1 > \dots > i_n} a_{i_1 \dots i_n}(x)[/tex]
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