I am trying to find double inverse Fourier transform of $$\exp\left({A \large\frac{\varepsilon^2 \xi^2+\eta^2}{\xi^2+\eta^2}}\right),$$ where $A$ is constant, $\varepsilon$ is positive number and $\xi$ and $\eta$ are Fourier parameters.I checked the Fourier Transform table but there isn't a Fourier or inverse Fourier transform correspond to this transform. Does anyone have an idea for evaluating inverse Fourier of this function?
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