The term "poweroid" has at least two meanings. Sheffer sequences are sometimes called poweroids (Steffensen 1941, Shiu 1982, Di Bucchianico and Loeb 2000). Jackway and Deriche (1996) and Jackway (2002) use the term to mean a function of the form


The case alpha=2 corresponds to the paraboloid and the case alpha=4 is sometimes called a quartoid (Jackway and Deriche 1996).

See also

Paraboloid, Quartoid, Sheffer Sequence

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Di Bucchianico, A. and Loeb, D. "A Selected Survey of Umbral Calculus." Electronic J. Combinatorics Dynamical Survey DS3, 1-34, April 2000., P. T. "Partial Orderings and Scale-Spaces with Monotonicity of Features." In Proceedings of ISMM2002 (Ed. H. Talbot and R. Beare). CSIRO Publishing, pp. 277-282, 2002.Jackway, P. T. and Deriche, M. "Scale-Space Properties of the Multiscale Morphological Dilation-Erosion." IEEE Trans. Patterns Anal. Mach. Intell. 18, 38-51, 1996.Shiu, E. S. W. "Steffensen's Poweroids." Scand. Actuar. J. 2, 123-128, 1982.Steffensen, J. F. "The Poweroid, an Extension of the Mathematical Notion of Power." Acta Math. 73, 333-366, 1941.

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Cite this as:

Weisstein, Eric W. "Poweroid." From MathWorld--A Wolfram Web Resource.

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