# Double Fourier Series $\cos(nx)\cos(my)$

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 $[-\pi /2,\pi /2]$.

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then?.......... – Xiaolang Apr 12 '13 at 2:40
Sorry I forgot a part of it – Username Unknown Apr 12 '13 at 2:41
Your title doesn't match your definition of $f$. – Stefan Smith Apr 12 '13 at 3:40
Could you briefly recall how the Fourier cosine-cosine series is defined? – 1015 Apr 12 '13 at 3:46
I am unsure what you are asking because it is a long summation that consist of sines and cosines and sine-cosine and cosine-sine and cosine-cosine and sine-sine. – Username Unknown Apr 12 '13 at 3:50