Modified Bessel Functions Relation

Hello,

A basic relation between modified Bessel functions exists,

$K_n(x) = \frac{1}{2}\pi\frac{I_{-n}(x)-I_n(x)}{sin(n\pi)}$

I am wondering if there is a similar relation for more advanced cases, such as $K_n(ax^b) = ???$, or if there is a straightforward way to go about determining the solution.

Thanks