# Fourier series

### noun Mathematics.

an infinite series that involves linear combinations of sines and cosines and approximates a given function on a specified domain.

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## Origin of Fourier series

First recorded in 1875–80; see origin at Fourier analysis

## Words nearby Fourier series

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2020

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## British Dictionary definitions for Fourier series

Fourier series

### noun

an infinite trigonometric series of the form 1/2 a 0 + a 1 cos x + b 1 sin x + a 2 cos 2 x + b 2 sin 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 coefficients

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Scientific definitions for Fourier series

Fourier series

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.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.