MATLAB: Problem with double sums

double sums

how to write this function in MATLAB knowing that if I separate the two sums as I wrote one tends to infinity.

The first idea I wrote

then check my code in some values of f as an example

but the result is

because

doc mean
doc var

If the ultimate goal is to compute the integral, you can consider using integral2

If you have to do it with sum, then since you already computed u2 for all values, it is just

x=[-20:0.2:10]; y=[-10:0.2:5]'; u2=-3*exp(-sqrt(x.^2+y.^2)/2);
sum(u2(:))*0.2*0.2

Note that you have to transpose x or y so it forms a grid

HTH