In Weinberg's book The Quantum Theory of Fields, volume 1 on p.387, there is a Fourier transform as:
$$\mathscr{E}(\mathbf{x},\mathbf{y})=(2\pi)^{-3}\int{\mathrm{d}^3p\,e^{i\mathbf{p}\cdot (\mathbf{x}-\mathbf{y})}E(\mathbf{p})}$$ where $E(\mathbf{p})=\sqrt{\mathbf{p}^2+m^2}.$
I don't know how to understand or to calculate this Fourier thanrform properly.
And Weinberg claimed that $\mathscr{E}(\mathbf{x},\mathbf{y})$ can be written in terms of a Hankel function of negative order : $$\mathscr{E}(\mathbf{x},\mathbf{y})=\frac{m}{2\pi^2r}\frac{\mathrm{d}}{\mathrm{d}r }\big(\frac{1}{r}K_{-1}(mr)\big).$$
I am wondering what exactly $K_{-1}$ means, usually we denote Hankel function as $H$ and $K$ as the second kind of Modified Bessel functions.