Peano kernel theorem
= Peano kernel theorem
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The Peano kernel theorem represents a linear approximation error $L$ that annihilates polynomials below degree $r$ as
$$
L(f)=\int_a^bK(t)f^{(r)}(t)\,dt,
\qquad
K(t)=L\left(\frac{(x-t)_+^{r-1}}{(r-1)!}\right).
$$