Integral representation of modified Bessel function of the second kind

[ulriksvensson]

Hi all. I need an integral representation of $$z^{-\nu}K_{\nu}$$ of a particular form. For $$K_{1/2}$$ it looks like this:

$$z^{-\frac{1}{4}}K_{1/2}(\sqrt{z}) \propto \int_{0}^{\infty}dt\exp^{-zt-1/t}t^{-1/2}$$

How do I generalize this for arbitrary $$\nu$$? A hint is enough, maybe there's a generating function one can use?

//Ulrik

 

[mehdi.naruei]

Hi
The general form is attached.