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Summation notation

  1. Mar 11, 2007 #1

    [tex]\sum_{u,v} H_{i-u,j-v}F_{u,v}[/tex]

    the same as

    [tex]\sum_u\sum_v H_{i-u,j-v}F_{u,v}[/tex]


    (Don't worry about what H,F,i,j,u,v are. I'm only asking about the notation.)
    Last edited: Mar 11, 2007
  2. jcsd
  3. Mar 11, 2007 #2
    I only see this in the case that there could be no confusion about the range of the indicies, and so I would say yes, they are the same.
  4. Mar 11, 2007 #3
    Yes, thanks, assuming that the ranges of the indices are unambiguous...

    I read the first form in a textbook; the context is applying convolution to image data, and I don't see any way to interpret it other than as a double summation. I just wanted some reassurance that I'm not overlooking something.
  5. Mar 11, 2007 #4


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    It's written that way to save space. Similar to writing [tex]\int f \, dV [/tex] rather than [tex]\int \int \int f \, dx\, dy\, dz [/tex]
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