Truncated power function ($(x-t{)}_{+}^r$)

For integer $r\ge 1$, the truncated power is zero for $x\le t$ and equals $(x-t{)}^r$ for $x>t$. It is globally $C^{r-1}$ and its $r$th derivative has a jump at $t$. Order zero is the step-function convention $1_{\{x>t\}}$. Knot divided differences of these functions produce B-splines.