Is it possible to evaluate the following integral?

$$\int \frac{(x-x_0) \: dx \: dy \: e^{i k_x x + i k_y y}}{((x-x_0)^2+(y-y_0)^2+4 h^2)^{\frac{5}{2}}}$$

As a first try, I evaluated

Integrate[Exp[I ky y]/(A + (y - y0)^2)^(5/2), {y, -Infinity, Infinity}]

However, it didn't work.

Any answer is highly appreciated.

  • $\begingroup$ Have you looked at FourierTransform? $\endgroup$ – bill s Apr 15 '18 at 15:55

Here's one way to approach this sort of thing: start simple and make it more complex as you go:

FourierTransform[1/t^2, t, w]

returns an answer just fine. So make it more complicated:

FourierTransform[1/(t - t0^2), t, w]

also works. Increase complexity:

FourierTransform[1/(a + (t - t0^2)), t, w]

still OK. Once more:

FourierTransform[1/(a + (t - t0^2))^(5/2), t, w]

wait a while, and you'll get an answer. Now your turn, but in 2D (still with FourierTransform).

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