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Truncated power function

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Definition

The truncated power function[1] with exponent is defined as

Alternatively, you may consider the subscript plus as an individual function with

and interpret the exponent as conventional power.

Relations

  • Truncated power functions can be used for construction of B-Splines.
  • is the Heaviside function.
  • where is the indicator function.
  • Truncated power functions are refinable.

References

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