Difference of Gaussian vs LoG

Hello

I am trying to approximate the log using the dog but i am not getting the right results. The notes here mention that it can be approximated by setting the sigma as shown below. I did a surf plot of the log and dog i constructed but they were not close. Also, the log generated by fspecial does not sum up to zero.

sigma = 5;
sigma1 = sigma/sqrt(2);
sigma2 = sigma*sqrt(2);

LoG = fspecial('log', 2*floor(3*sigma)+1, sigma);

% Generate LoG
DoG1 = fspecial('gaussian', 2*floor(3*sigma1)+1, sigma1);
DoG2 = fspecial('gaussian', 2*floor(3*sigma2)+1, sigma2);

DoG = DoG1 - DoG2;

I hope someone can help me on this