We consider the function $f$ defined by: $\forall (x,y) \in \mathbb{R}^2,\ f(x,y) = \frac{1}{1+x^2+y^2}$. Show that $\hat{f}$ is defined on $\mathbb{R}^2$ with $\hat{f}(q,\theta) = \frac{\pi}{\sqrt{1+q^2}}$.
We consider the function $f$ defined by: $\forall (x,y) \in \mathbb{R}^2,\ f(x,y) = \frac{1}{1+x^2+y^2}$.
Show that $\hat{f}$ is defined on $\mathbb{R}^2$ with $\hat{f}(q,\theta) = \frac{\pi}{\sqrt{1+q^2}}$.