What Is the Fourier Transform of the Density Matrix of cos(x+y)*cos(x-y)?

[kd6ac]

Fourier transform of density matrix of cos(x+y)*cos(x-y)

I would like to know whether there exists a solution to the following integral,

$$\frac{1}{\pi} \int\limits_{-\infty}^{\infty} \cos(x+y)^\alpha \cos(x-y)^\alpha e^{2ipy}$$

The above expression is the Fourier transform of the off-diagonal elements of the density matrix,

$$\rho = \cos(x+y)^\alpha \cos(x-y)^\alpha$$

Any advice, or reference to books/articles, would be greatly appreciated.

 

[mathman]

Start by defining the domain for α.
Google "Fourier integral tables" should help.