Back to e

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Back to e

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Back to e

Above, we defined $e$ as the particular real number satisfying

\

which gave us $(a^x)^\ when $a=e$. From this expression, we have, as $\,
\


or,
\

This is one way to define $e$. Another way to arrive at the same definition is to ask what logarithmic base $e$ gives that the derivative of$\ is $1/x$. We denote $\ by $\.

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