Truncated power function explained

In mathematics, the truncated power function[1] with exponent

n

is defined as
n
x
+

=\begin{cases}xn&:x>0\\ 0&:x\le0. \end{cases}

In particular,

x+=\begin{cases}x&:x>0\\ 0&:x\le0. \end{cases}

and interpret the exponent as conventional power.

Relations

x\mapsto

0
x
+
is the Heaviside function.

\chi[a,b)(x)=

0
(b-x)
+

-

0
(a-x)
+
where

\chi

is the indicator function.

See also

External links

References

  1. Book: Massopust , Peter. Interpolation and Approximation with Splines and Fractals. Oxford University Press, USA. 2010. 978-0-19-533654-2. 46.