Thread: Simplifying a ratio of modified Bessel functions of the second kind

I found the following solution to a differential equation problem but need to simplify it:

K0(A*x)/K0(A*B)

where K0 is the modified Bessel function of the second kind with alpha = 0, x is the independent variable, and A and B are constants. I'm only interested in the interval x>=B.

So far, I've tried to use the definitions of the Bessel functions to replace K0s with I0s with J0s, or K0s with H0s with J0s, but I frequently wind up with zeroes top and bottom. Any tips or solutions?

Originally Posted by penguinick

I found the following solution to a differential equation problem but need to simplify it:

K0(A*x)/K0(A*B)

where K0 is the modified Bessel function of the second kind with alpha = 0, x is the independent variable, and A and B are constants. I'm only interested in the interval x>=B.

So far, I've tried to use the definitions of the Bessel functions to replace K0s with I0s with J0s, or K0s with H0s with J0s, but I frequently wind up with zeroes top and bottom. Any tips or solutions?

If and are arbitrary constants in the solution, then set then you have

CB

Originally Posted by CaptainBlack

If and are arbitrary constants in the solution, then set then you have

CB

Nice... but there's no way to reduce it into something that doesn't have infinite series, I take it?