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In mathematics, the '''truncated power function'''<ref>{{cite book
|title=Interpolation and Approximation with Splines and Fractals
|first=Peter|last=Massopust
|publisher= Oxford University Press, USA
|year=2010
|isbn=978-0-19-533654-2
|page=46
}}</ref> 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 function|power]].
==Relations==
* Truncated power functions can be used for construction of [[B-spline]]s.
* <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 function|refinable]].
== See also ==
* [[Macaulay brackets]]
==External links==
*[http://mathworld.wolfram.com/TruncatedPowerFunction.html Truncated Power Function on MathWorld]
==References==
<references/>
[[Category:Numerical analysis]]
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