Let $f(x,y) = xy$ on the square $[0, \pi]^2$. Find the Fourier cosine-cosine series of $f$.
I am working on this question with a group and one of us gets all the coefficients as zero. Is this correct or not?
Also, we are at a disagreement about whether to integrate over $[-\pi,\pi]$ or $[-\pi /2,\pi /2]$.