Truncated power function

In mathematics, the truncated power function with exponent $$n$$ is defined as


 * $$x_+^n =

\begin{cases} x^n &:\ x > 0 \\ 0 &:\ x \le 0. \end{cases} $$

In particular,
 * $$x_+ =

\begin{cases} x &:\ x > 0 \\ 0 &:\ x \le 0. \end{cases} $$ and interpret the exponent as conventional power.

Relations

 * Truncated power functions can be used for construction of B-splines.
 * $$x \mapsto x_+^0$$ is the Heaviside function.
 * $$\chi_{[a,b)}(x) = (b-x)_+^0 - (a-x)_+^0$$ where $$\chi$$ is the indicator function.
 * Truncated power functions are refinable.