Summation notation

1. Mar 11, 2007

gnome

Is

$$\sum_{u,v} H_{i-u,j-v}F_{u,v}$$

the same as

$$\sum_u\sum_v H_{i-u,j-v}F_{u,v}$$

?

Last edited: Mar 11, 2007
2. Mar 11, 2007

Crosson

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. Mar 11, 2007

gnome

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. Mar 11, 2007

AlephZero

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