Truncated Power Function

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

:$x_+^n = \begin x^n &:\ x > 0 \\ 0 &:\ x \le 0. \end$

In particular,
:$x_+ = \begin x &:\ x > 0 \\ 0 &:\ x \le 0. \end$
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_{ ,b)}(x)_=_(b-x)_+^0_-_(a-x)_+^0_where_$\chi$_is_the_indicator_function.
*_Truncated_power_functions_are_refinable_function.html" ;"title="indicator_function.html" ;"title=",b)}(x) = (b-x)_+^0 - (a-x)_+^0 where $\chi$ is the indicator function">,b)}(x) = (b-x)_+^0 - (a-x)_+^0 where $\chi$ is the indicator function.
* Truncated power functions are refinable function">refinable.

See also

* Macaulay brackets

External links

Truncated Power Function on MathWorld

References

Numerical analysis