Let be function such that . Furthermore let have the charcteristic that . Now it is pretty clear that except possibly at , but in fact is continuous at all these points due to its eveness. Next note that , in other words its posses a right and left hand limit everywhere. So since noting all of these things we may conclude that where is the Fourier Series given by.

Where

And as was stated above

So

Now letting gives

So now consider when we are left with

Solving gives

So then we get finally that

Note from this we can also glean that