I just have a quick question:
I'm evaluating a Fourier coefficient for the following series:
I'm going to show my work:
I said that
This is what I did to simplify what was in the brackets:
Multiplying by , I get:
Now this is where I'm somewhat in the dark. Since I'm plugging in values of n, where , into , I notice when n is odd, I get either 1 or -1, and when n is even, I get zero. Thus, I rewrote my answer as:
I noticed that could be written as
So then I saw that
Thus, my series solution would be
Is this correct??
However, my question is this: when I rewrote as , do I need to replace the other n's in my equation with 2n-1? meaning, would my answer for be ????
I'd appreciate any help.