Norm of modified bessel function

paweld

How to compute norm of the modified bessel function of imaginery order. I mean the following integral:
[tex]
\int_0^\infty \frac{1}{z} K_{in}^2(z)dz
[/tex]
I found it in Fulling article in Phys.Rev.D.7.2850 (but I can't prove it) that this integral equals:
[tex]
\frac{\pi^2}{2n \textrm{sinh}(2\pi n)}
[/tex]