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i can show $\sum |x|^2=\int_a^b|f(x)|^2dx$ in term of integral, or this one $|\sum x\overline y|^2=|\int_a^bf(x)\overline {g(x)}dx|^2$ but i don't know how to show this one $\sum_{i}^{n-1}\sum_{j=i+1}^{n}|(x_i\overline y_j-x_j\overline y_i)|^2$ in term of integral

$\sum_{i}^{n-1}\sum_{j=i+1}^{n}|(x_i\overline y_j-x_j\overline y_i)|^2=?$

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What are the functions $f,g$, and the numbers $a,b$? What are $x,y$ in your sums? What are you summing over in $\sum |x|^2$? – Eckhard Dec 28 '12 at 17:38
How was this question upvoted? As it's written, it makes no sense to me. I downvoted. – mixedmath Dec 29 '12 at 8:36

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