Definition:Bessel's Equation

Equation
Bessel's equation is a second order ODE of the form:
 * $\displaystyle x^2 \frac{\mathrm d^2 y} {\mathrm d x^2} + x \frac{\mathrm d y} {\mathrm d x} + \left({x^2 - p^2}\right) y = 0$

The parameter $p$ may be any arbitrary real or complex number.

Solution
The solutions of Bessel's equation are known as Bessel functions, and they are functions of the parameter $p$.