Summation notation

  • Thread starter gnome
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  • #1
gnome
1,037
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Is

[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:

Answers and Replies

  • #2
Crosson
1,259
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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.
 
  • #3
gnome
1,037
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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.
 
  • #4
AlephZero
Science Advisor
Homework Helper
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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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