- #1

Ansatz7

- 29

- 0

**Homework Statement**

Calculate the Fourier transform of f(x) = (1 + |x|

^{2})

^{-1}, x[itex]\in[/itex]ℝ

^{3}

**The attempt at a solution**

As far as I can tell, the integral we are supposed to set up is:

Mod note: Fixed your equation. You don't want to mix equation-writing methods. Just stick to LaTeX.

$$\int \frac{e^{-2\pi i (\vec{k}\cdot\vec{x})}}{1+|\vec{x}|^2}dV = \int \frac{e^{-2\pi i r(k_1\sin\theta\cos\phi + k_2 \sin\theta\sin\phi + k_3\cos\theta)}}{1+r^2} r^2\sin\theta\,d\theta\,d\phi\,dr$$but I have no idea how to perform this integral. Any ideas appreciated! (Also, sorry about the fractions - I have no idea why they aren't working because I have no tex experience).

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