It basically boils down to:
show that:
$$\int_{-\infty}^{\infty} dy \frac{J_1 \left ( \pi\sqrt{x^2+y^2} \right )}{\sqrt{x^2+y^2}} = \frac{2 \sin{\pi x}}{\pi x} $$
My life story (somewhat irrelevant):
A jinc function is besselj(1,pi*r)/( 2r ), a sinc is sin(pi*x) / (pi*x)
I have noticed, while...