= Lee interpolation identity
{c}
{title2=$\ell_{i+1}-\ell_i=\omega_iN_i$}
= Lee's formula
{c}
{synonym}
For distinct increasing knots, let $\ell_i(\cdot,t)$ interpolate $(\cdot-t)_+^{k-1}$ on $t_i,\ldots,t_{i+k-1}$ and let $\omega_i(x)=\prod_{r=1}^{k-1}(x-t_{i+r})$. Adjacent interpolants share $k-1$ values; their difference is a multiple of $\omega_i$. Its leading coefficient, by the <divided difference> recurrence, is the order-$k$ <B-spline> $N_i(t)$. Thus $\ell_{i+1}(x,t)-\ell_i(x,t)=\omega_i(x)N_i(t)$. Telescoping proves the <Marsden identity>. Repeated knots require the well-defined confluent or limiting convention.
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