Fourier series

American  

noun

Mathematics.

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

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Fourier series British  

noun

1. 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

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Fourier series Scientific  

1. 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.

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Etymology

Origin of Fourier series

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

Example Sentences

Mathematically, the book incorporates complex analysis, Fourier series, abstract algebra, and modern geometry.

From Scientific American • Sep. 14, 2015

The epicycles represented nothing more nor less than the first terms in the Fourier series, which in the last century has become a basis of such calculations, both in astronomy and physics generally.

From History of Astronomy by Forbes, George