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Taylor Series Expansions

A Taylor series expansion of a continuous function $ f(x)$ is a polynomial approximation of $ f(x)$ . This appendix derives the Taylor series approximation informally, then introduces the remainder term and a formal statement of Taylor's theorem. Finally, a basic result on the completeness of polynomial approximation is stated.



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``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 © 2014-04-21 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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