\begin{definition}[Definition:Modified Bessel Function]
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 $K_n$.
\end{definition}