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

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