Truncated power function

In the mathematical subfield of numerical analysis the truncated power function is a generalization of the indicator function.

Definition

Given a function f the truncated power function is defined as

$f_{+}^{n}:=\left\{{\begin{matrix}f^{n}&{\mbox{if}}\ f\geq 0\\0&{\mbox{if}}\ f<0\end{matrix}}\right.$

Notes

$\chi _{(a,b]}(x)=(b-x)_{+}^{0}-(a-x)_{+}^{0}$