Truncated power function

In mathematics, the truncated power function[1] with exponent $n$ is defined as

x_{+}^{n}={\begin{cases}x^{n}&:\ x>0\\0&:\ x\leq 0.\end{cases}}

In particular,

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.
$x\mapsto x_{+}^{0}$ is the Heaviside function.
$\chi _{[a,b)}(x)=(b-x)_{+}^{0}-(a-x)_{+}^{0}$ where $\chi$ is the indicator function.
Truncated power functions are refinable.

See also

Macaulay brackets

External links

Truncated Power Function on MathWorld

References

Massopust, Peter (2010). Interpolation and Approximation with Splines and Fractals. Oxford University Press, USA. p. 46. ISBN 0-19-533654-2.

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