Cubic cardinal B-spline ($B_3(s)=\frac{1}{6}{\sum }_{j=0}^4(-1{)}^j(\genfrac{}{}{0ex}{}{4}{j})(s-j{)}_{+}^3$)

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.