Definite integral of cosines multiplied by a gaussian

I would like to solve the following integral:

$$\int_0^L dx \int_0^L dy \quad e^{-a(x-y)^2+b(x-y)}\cos(\frac{n\pi x}{L})\cos(\frac{n\pi y}{L})$$

Does anybody have a clue on how to proceed? Thanks

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This will be messy, in terms of error functions of a complex argument. –  Ron Gordon Mar 22 '13 at 13:58