\begin{definition}[Definition:Bessel Function]
The '''Bessel functions''' are solutions to Bessel's 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 Bessel functions of the first kind $J_n$
and:
:the Bessel functions of the second kind $Y_n$.
\end{definition}