### Fourier series expansion

(type of series expansion of a function using trigonometric functions)

The **Fourier series expansion** of a periodic function or a function
over a limited interval is the function's **series expansion**
consisting of the function's equivalent **Fourier series**.
The terms of the series are called the **Fourier coefficients**,
and for an arbitrary function, they can be calculated using
the **Fourier transform**. The *Fourier coefficients*
of a particular function may be described as "within
**Fourier space**" or "within the **Fourier domain**"
(though these phrases often are used with more particular meanings,
e.g., the term *space* is generally used for a variant of Fourier
series expansion of two or three dimensional functions).

As a Fourier series, the Fourier series expansion may be written
in terms of trigonometric functions or alternately in equivalent
exponential functions (as per **Euler's formula**) and may
use **complex numbers** to include representation of phase information.

(*mathematics*)
**Further reading:**

http://en.wikipedia.org/wiki/Fourier_series

http://en.wikipedia.org/wiki/Euler%27s_formula

**Referenced by pages:**

Fourier series

Index