Truncated power function

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

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

In particular,

x_{+} = {\begin{matrix} x & : x > 0 \\ 0 & : x \leq 0. \end{matrix}

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.
$χ_{[a, b)} (x) = (b - x)_{+}^{0} - (a - x)_{+}^{0}$ where $χ$ is the indicator function.
Truncated power functions are refinable.

^ Page Module:Citation/CS1/styles.css has no content.Massopust, Peter (2010). Interpolation and Approximation with Splines and Fractals. Oxford University Press, USA. p. 46. ISBN 978-0-19-533654-2.