Positive Integer Exponents

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Positive Integer Exponents

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Positive Integer Exponents

The “original” definition of exponents which “actually makes sense” applies only to positive integer exponents:

\

where $a>0$ 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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