= Simple-knot B-spline regularity
{title2=$N_{i,k}\in C^{k-2},\quad\operatorname{supp}N_{i,k}=[t_i,t_{i+k}]$}
For distinct increasing knots and $k\ge2$, the explicit <divided difference> formula writes an order-$k$ <B-spline> as a finite sum of <truncated power functions> of degree $k-1$. It is a <piecewise polynomial function> and is globally $C^{k-2}$. Below its first knot the order-$k$ <divided difference> annihilates a degree-$k-1$ polynomial; above its last knot all values vanish. Nonzero first and last pieces give the exact closed support. Order one gives interval indicators instead of continuous splines.
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