I need to find the Fourier coefficients ($G_{pq}$) of the following equation
$$ \alpha e^{-\beta y} = \sum_{p=1}^\infty\sum_{q=1}^\infty\ G_{pq} \cos(px)[\frac{\cos(qy) + \sin(qy) - e^{-\beta y}}{q^2}] - \sum_{p=1}^\infty\sum_{q=1}^\infty G_{pq}\cos(px)\cos(qy) $$
How to particularly handle the exponential term ? Is there some sort of expansion I need to consider ?