Fourier series

A Fourier series is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.

For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.
This application is possible because the derivatives of trigonometric functions fall into simple patterns.
Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always converge.

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