= Distributional jump formula for a Heaviside product
{title2=$D^k(Hu)=Hu^{(k)}+\sum_{s=0}^{k-1}u^{(k-1-s)}(0)\delta_0^{(s)}$}
For a <smooth function> $u$, the <distributional derivative> of the product of $u$ with the <Heaviside function> is $D(Hu)=Hu'+u(0)\delta_0$. Induction gives the displayed formula. It records all boundary sources, including derivatives of the <Dirac delta distribution>, and determines which initial derivatives must vanish in a <retarded fundamental solution>.
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