# Fourier series

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Related to Fourier cosine series: Fourier expansion, Fourier sine series

## Fourier series

n.
An infinite series whose terms are constants multiplied by sine and cosine functions and that can, if uniformly convergent, approximate a wide variety of functions.

[After Baron Jean Baptiste Joseph Fourier.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## Fourier series

n
(Mathematics) an infinite trigonometric series of the form a0 + a1cos x + b1sin x + a2cos 2x + b2sin 2x + …, where a0, a1, b1, a2, b2 … are the Fourier coefficients. It is used, esp in mathematics and physics, to represent or approximate any periodic function by assigning suitable values to the coefficients
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## Fou′rier se`ries

n.
an infinite series that approximates a given function on a specified domain by using linear combinations of sines and cosines.
[1875–80; see Fourier analysis]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Fourier series - the sum of a series of trigonometric expressions; used in the analysis of periodic functionsseries - (mathematics) the sum of a finite or infinite sequence of expressions
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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Each of the displacement amplitude functions U(x, y, z), V(x, y, z), and W(x, y, z) is expressed, respectively, in the form of a three-dimensional (3D) Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities of the displacement function and its derivatives at the edges; that is,
Moreover, [F.sup.e.sub.p] can be expanded into the Fourier cosine series. Considering the partial sum, the Fejersum, and theVallee-Poussinsum [5,7,14] of the Fourier cosine series of [F.sup.e.sub.p], we will obtain the approximation of the original function f on [OMEGA] by cosine polynomials.

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