Suppose the function f(x) is defined on the interval (-L,L) and

is finite.

We want to approximate f(x) by a finite series of (co-)sines:

where parameters

,

, and

are freely variable.

The mean square error of the approximation is defined as:

a) Show that the choice:

,

and

, where

,

, and

are the Fourier coefficients of f, minimizes

I think I can figure the rest of it out when I get this, so I won't bother typing it... I have never worked with the mean error before so I'm a bit confused as to how to start. Any help would be appreciated.