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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