Definition:Modified Bessel Function

Definition
The modified Bessel functions are solutions to Bessel's modified equation:
 * $x^2 \dfrac {\d^2 y} {\d x^2} + x \dfrac {\d y} {\d x} - \paren {x^2 + n^2} y = 0$

These solutions have two main classes:
 * the modified Bessel functions of the first kind $I_n$

and:
 * the modified Bessel functions of the second kind $K_n$.

Also known as
Some sources use $p$ to denote the order of the modified Bessel function.