We are creating the world's most trusted encyclopedia and knowledge base.
Once you join us and log in, you'll be able to edit this page instantly!

Fourier series

From Citizendium, the Citizens' Compendium

Jump to: navigation, search
Image:Statusbar3.png
Main Article
Talk
Definition [?]
Related Articles  [?]
Bibliography  [?]
External Links  [?]
 
This is a draft article, under development. These unapproved articles are subject to a disclaimer.

In mathematics, the Fourier series, named after Joseph Fourier (1768—1830), of a complex-valued periodic function f of a real variable, is an infinite series

\sum_{n=-\infty}^\infty c_n e^{2\pi inx/T}

defined by

c_n = \frac{1}{T} \int_0^T f(x) \exp\left(\frac{-2\pi inx}{T}\right)\,dx,

where T is the period of f.

In what sense it may be said that this series converges to f(x) is a somewhat delicate question.

Retrieved from "http://en.citizendium.org/wiki/Fourier_series"
Views
Personal tools