One often finds in the literature a derivation of the Laplacian of a Gaussian (LoG) that s...

One often finds in the literature a derivation of the Laplacian of a Gaussian (LoG) that starts with the expression

where r2 = x2 + y2. The LoG is then found by taking the second partial derivative: ∇2G(r) = ∂2G/∂r2. Finally, x2+ y2is substituted for r2 to get the (incorrect) result

Derive this result and explain the reason for the difference between this expression and Eq. (10.2-23).

(10.2-23)