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## integration – how decipher a double integral analytically or numerically

can somebody ameliorate me to decipher this integral or elucidate me the best way to clique it on mathematica?

commence{equation}

int_{-infty}^{+infty} dk_alpha dk_phi frac{1}{2pi} e^{-frac{k_alpha^2}{2}} e^{-frac{k_phi^2}{2}} e^{ik_alpha alpha} e^{ik_phi phi} xi^{ik_alpha} e^{2isqrt{k_alpha^2 – xi k_phi^2}} e^{-2i k_alpha arctanh{ Big( frac{sqrt{k_alpha^2 – xi k_phi^2}}{k_alpha}} Big) }

aim{equation}

I’ve tried each analytically and numerically however I could not decipher it.

Analytically the calculation would not appear to refer on, whereas numerically it returns a number of mistake messages.

Thank you all!

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