# Simplifying some sums

Is there any simplification/approximation for the following equation:

∑i∑jA(i,j)−2∑i∑jB(i,j)A(i,j)+2∑i∑jB(i,j)\sum_i\sum_j A(i, j) -2 \sum_i\sum_jB(i,j)A(i,j) + 2\sum_i\sum_jB(i,j)

where A(i,j)=(i−c+j)A(i,j) = (i-c + j) and B(i,j)=ln(i−c+j)B(i,j) = \ln(i-c+j) with cc a constant.

I am trying to transform this equation in some way but I am not sure there is actually something I can do here.

EDIT : for the summations, we have i=0,…ti =0, \dots t and j=c+1−i,…,min(c,i,t−i)j = c+1-i, \dots, \min(c, i, t-i).

Comment : If we regroup the sums, we end up with something of the form A−2AlnA+2lnA A -2A\ln A +2\ln A but I am not sure what we can do about this.

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What are the summation limits?
– user58697
2 days ago

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