How are you supposed to verify or derive common physics text 'identities' involving dirac deltas like $$ \lim_{t \to 0} \mbox{sign}(t) \frac {\partial}{\partial t} \frac{\partial}{\partial x^i} \delta(|\mathbf x|^2-t^2) = 2 \pi \frac{\partial}{\partial x^i} \delta(\mathbf x) $$ Replacing delta with things like $\lim_{a\to 0} \frac{1}{a\sqrt \pi} e^{-(x/a)^2}$ gets me nowhere. Can this be seen just from test functions?
2026-03-31 15:15:46.1774970146
Identities with dirac deltas
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