= Cubic cardinal B-spline
{title2=$B_3(s)=\frac16\sum_{j=0}^4(-1)^j\binom4j(s-j)_+^3$}
This degree-three <Cardinal B-spline> has support $[0,4]$, is twice continuously differentiable, and has values $0,1/6,2/3,1/6,0$ at the consecutive integer knots. Their sum is one. Its <truncated power function> representation has coefficients whose first four moments vanish, making it zero after its final knot. Four knot intervals are the minimum possible compact support for a nonzero cubic $C^2$ <spline>: with fewer intervals the four moment constraints form a full-column-rank <Vandermonde matrix>. Translating and rescaling this function gives a local <basis> for cubic <spline interpolation> on a uniform mesh.
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