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**wudup** Could someone please shed some light on how I might show that

$\displaystyle \lim_{\epsilon\to 0}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}{\epsilon\over 2\pi [(x-x')^2+(y-y')^2+\epsilon^2]^{3\over2}}f(x,y)\;dx\,dy\,\,=f(x',y')$? I am not sure what conditions there is on $\displaystyle f(x,y)$, though I do know that $\displaystyle \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}{z\over 2\pi [(x-x')^2+(y-y')^2+z^2]^{3\over2}}f(x,y)\;dx\,dy$ is well-defined (converges) for all $\displaystyle x,y\in R$ and $\displaystyle z>0$.

Brainstorm: Perhaps we can show that $\displaystyle \lim_{\epsilon\to 0}{\epsilon\over 2\pi [(x-x')^2+(y-y')^2+\epsilon^2]^{3\over2}}$ is the Delta function $\displaystyle \delta(x-x')\delta(y-y')$? Or maybe changing variables?

Thanks.