Cardinal B-spline

Let $n$ be a non-negative integer and $x$ a real number, this application evaluates the cardinal B-spline $B_n(x)$ and the first derivative $B'_n(x)$. If $n\geqslant 3$, it also evaluates the second derivative $B''_n(x)$ of the cardinal B-spline.

Note that in this calculator the B-slines use zero-based indexes and $B_n(x)$ are central support in $\displaystyle\left[-\frac{(n+1)}{2},\frac{(n+1)}{2}\right]$, i.e. $B_n(x)$ is zero if $\displaystyle x<-\frac{(n+1)}{2}$ or $\displaystyle x>\frac{(n+1)}{2}.$

Cardinal B-spline Calculator