Definition:Bessel Function

Definition
The Bessel functions are solutions to Bessel's Equation
 * $x^2 \dfrac{\mathrm d^2 y} {\mathrm d x^2} + x \dfrac{\mathrm d y} {\mathrm d x} + \left({x^2 - p^2}\right) y = 0$

These solutions have two main classes, the Bessel functions of the first kind $J_p$ and Bessel functions of the second kind $Y_p$.

Bessel Function of the First Kind
The Bessel Function of the First Kind is a Bessel function which is nonsingular at the origin.

Bessel Function of the Second Kind
The Bessel Function of the Second Kind is a Bessel function which is singular at the origin.