Truncated power function

Definition

The truncated power function with exponent $n$ is defined as

$x_{+}^{n}={\begin{cases}x^{n}&:\ x\geq 0\\0&:\ x<0.\end{cases}}$

Alternatively, you may consider the subscript plus as an individual function with

$x_{+}={\begin{cases}x&:\ x\geq 0\\0&:\ x<0.\end{cases}}$

and interpret the exponent as conventional power.

Notes

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

External links

• Truncated Power Function on MathWorld