The function is: $K(z)= \dfrac{e^{i\sqrt{(z-z')^2+C}}}{\sqrt{(z-z')^2+C)}}$ where $C$ and $z'$ are constants. $C=R^2 + A^2-2RA\cos(\theta)$. This is the kernel in the integral equation of the current distribution in a cylindrical antenna. To find the fourier transform, I multiply by $e^{i\lambda t}$ and I need to take the integral from $-\infty$ to $\infty$. so $K(\lambda)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} K(z) e^{i\lambda z} dz$. I used Gradshteyn and Ryzhik table book but to no avail.
The answer I have is: $\frac{i}{2} H_0^{(1)}(\sqrt{1-\lambda^2}\sqrt{C})$ But I have no clue how it is done though I made few unsuccessful substitutions.