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How to interpret a Summation and Cartesian product together in a formula

  1. Oct 13, 2011 #1
    Hi all,

    [tex]\sum_{i=1}^n k_i \Pi_{i=1}^n O_i(\mu)[/tex]

    How to interpret this equation.
     
    Last edited: Oct 13, 2011
  2. jcsd
  3. Oct 13, 2011 #2

    HallsofIvy

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    Actually the way it is written makes it ambiguous. The index should not be "i" in both. My best guess is that better notation would be
    [tex]\sum_{i=1}^n k_i \Pi_{j=1}^n O_j(\mu)[/tex]
    in which case we could take the product outside the sum so it would be just
    [tex]\left(\sum_{i=1}^n k_i\right)\left(\Pi_{j=1}^n O_j(\mu)\right)[/tex]
    and now, since the sum and product are separated, we could write that as
    [tex]\left(\sum_{i=1}^n k_i\right)\left(\Pi_{i=1}^n O_i(\mu)\right)[/tex]

    Perhaps that is what is meant.
     
  4. Oct 13, 2011 #3
    Thank you so much HallsofIvy.
     
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