Integral representation of modified Bessel function of the second kind

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

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

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

//Ulrik
 

Answers and Replies

  • #2
Hi
The general form is attached.
 

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