Poweroid
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 SequenceExplore with Wolfram|Alpha
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References
Di Bucchianico, A. and Loeb, D. "A Selected Survey of Umbral Calculus." Elec. J. Combin., Dynamic Survey DS3, Apr. 10, 2000. https://doi.org/10.37236/24.Jackway, 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.Referenced on Wolfram|Alpha
PoweroidCite this as:
Weisstein, Eric W. "Poweroid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Poweroid.html