# Fourier series

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Related to Fourier series: Fourier transform

## 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

*a*0 +*a*1cos*x*+*b*1sin*x*+*a*2cos 2*x*+*b*2sin 2*x*+ …, where*a*0,*a*1,*b*1,*a*2,*b*2 … 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 coefficientsCollins 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.

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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 |

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