Truncated power function

In mathematics, the truncated power function with exponent <math>n</math> is defined as

:<math>x_+^n =

\begin{cases}

x^n &:\ x > 0 \\

0 &:\ x \le 0.

\end{cases}

</math>

In particular,

:<math>x_+ =

\begin{cases}

x &:\ x > 0 \\

0 &:\ x \le 0.

\end{cases}

</math>

and interpret the exponent as conventional power.

Relations

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