how to interpret this double summation, the first from i=1 and the second from j does not equal i

Question

I'm not sure what the meaning of the double sum is in this formula.

I think it is more common and clearer to represent the second sum as $$\sum_{j=1\j \neq i}^N$$ where it is clear you sum over all the $j$s that are not equal to $i$ — Ross Millikan, Jul 21 '17 at 15:33

score 2 · Answer 1 · answered Jul 21 '17 at 15:22

2

If for instance $N=3$, you consider the terms s.t. $(i,j)=(1,2),(1,3),(2,1),(2,3),(3,1),(3,2)$

answered Jul 21 '17 at 15:22

Evargalo

2,593

1

thank you for answering – user342836 Jul 21 '17 at 19:48

score 1 · Answer 2 · answered Jul 21 '17 at 15:49

1

This notation is not really acceptable as it mixes two different conventions: the first summation specifies a range, while the second does not (it merely excludes the combinations with $i=j$).

I would have preferred one of

$$\sum_{i=1}^n\sum_{j=1\\j\ne i}^n$$ or $$\sum_i\sum_{j\ne i}$$

This said, it is equivalent to

$$\sum_{i=1}^n\left(\sum_{j=1}^{i-1}+\sum_{j=i+1}^n\right)$$

answered Jul 21 '17 at 15:49

thank you for answering – user342836 Jul 21 '17 at 19:48

how to interpret this double summation, the first from i=1 and the second from j does not equal i

2 Answers2