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In mathematics, the truncated power function [ 1]
n
{\displaystyle n}
x
+
n
=
{
x
n
:
x
>
0
0
:
x
≤
0.
{\displaystyle x_{+}^{n}={\begin{cases}x^{n}&:\ x>0\\0&:\ x\leq 0.\end{cases}}}
In particular,
x
+
=
{
x
:
x
>
0
0
:
x
≤
0.
{\displaystyle x_{+}={\begin{cases}x&:\ x>0\\0&:\ x\leq 0.\end{cases}}}
and interpret the exponent as conventional power .
Relations
Truncated power functions can be used for construction of B-splines .
x
↦
x
+
0
{\displaystyle x\mapsto x_{+}^{0}}
Heaviside function .
χ
[
a
,
b
)
(
x
)
=
(
b
−
x
)
+
0
−
(
a
−
x
)
+
0
{\displaystyle \chi _{[a,b)}(x)=(b-x)_{+}^{0}-(a-x)_{+}^{0}}
χ
{\displaystyle \chi }
indicator function .Truncated power functions are refinable .
See also
External links
References
^ Massopust, Peter (2010). Interpolation and Approximation with Splines and Fractals . Oxford University Press, USA. p. 46. ISBN 978-0-19-533654-2 
