(adsbygoogle = window.adsbygoogle || []).push({}); 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,

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

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

[tex] \rho = \cos(x+y)^\alpha \cos(x-y)^\alpha [/tex]

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

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# Fourrier transform of cos

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