The second-order ordinary differential equation
(1)
|
The solutions are the modified Bessel functions of the first and second kinds, and can be written
(2)
| |||
(3)
|
where is a Bessel function of the first kind, is a Bessel function of the second kind, is a modified Bessel function of the first kind, and is modified Bessel function of the second kind.
If , the modified Bessel differential equation becomes
(4)
|
which can also be written
(5)
|