Thread: fourier transform of the bessel function

1. fourier transform of the bessel function

hey, everybody!

Does anyone know how to calculate the fourier transform of

$\frac{J_1(\mid{x}\mid)}{\mid{x}\mid}$

where is the first order Bessel function of the first kind.

Any help would be very appreciated !

2. may be a easier one

To discrease the difficuty:

who knows how to compute :

$\int_{0}^{\infty}{J_1(x)}J_0({w}{x})\exp(-jx^2)dx$