Positive Integer Exponents

The ``original'' definition of exponents which ``actually makes sense'' applies only to positive integer exponents:

where is real.

Generalizing this definition involves first noting its abstract mathematical properties, and then making sure these properties are preserved in the generalization.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.