Fourier series

noun

, Mathematics.

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

Fourier series

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

Fourier series

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.

Word History and Origins

Origin of Fourier series¹

First recorded in 1875–80; Fourier analysis

Example Sentences

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

From Scientific American

I adapted methods from mathematical tools called Fourier series and complex analysis to create complex-valued wave functions that have a given, selected symmetry.

From Scientific American

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 Project Gutenberg