Ordinarily, I check my answers by plugging the problem into Wolfram Alpha. But I'm not aware of a way to do this when it comes to finding a Fourier Series of an equation or system of equations. This is especially true if it's a periodic set, as I have no idea how to supply the condition that $\displaystyle f(x + p) = f(x)$.

Is there any way to calculate this, either via Mathematica, MATLAB, Wolfram Alpha, or something else?