Hi, I am using the following function::
Refine[D[(Sum[((u[k, t] - u[k, t - 1])^2)/T, {k, 1, 10}, {t, 1, 5}] +
2*(Sum[Sum[(u[i, t] - u[i, t - 1])*(u[j, t] - u[j, t - 1]), {i,
1, 9}, {t, 1, 5}], {j, 2, 10}]/T)*F)^(1/2), u[1, 1]]]
Here, I am trying to eliminate the overlapping square terms in order to get the pure covariance variable from
2*(Sum[Sum[(u[i, t] - u[i, t - 1])*(u[j, t] - u[j, t - 1]), {i, 1, 9}, {t, 1, 5}], {j, 2, 10}]/T
I am trying to eliminate the resulting variables having same squared expressions of [(u[i,t]-u[i,t-1])(u[i,t]-u[i,t-1])] which contains the same element "i'. For example, I would like to eliminate something like (u[1,2]-u[1,1])*(u[1,2]-u[1,1]). I tried the functions "except" and "eliminate" but did not get the desired outcome at all. Could you please help me out with this critical problem..? Thank you so much in advance.
