Fourier Series - Approximation and Convergence of Fourier Series

Approximation and Convergence of Fourier Series

An important question for the theory as well as applications is that of convergence. In particular, it is often necessary in applications to replace the infinite series   by a finite one,

This is called a partial sum. We would like to know, in which sense does (SN ƒ)(x) converge to ƒ(x) as N tends to infinity.

Read more about this topic:  Fourier Series

Famous quotes containing the word series:

    The woman’s world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.
    Jeanine Basinger (b. 1936)