Definition:Bessel's Equation

Equation
Bessel's equation is a second order ODE of the form:
 * $x^2 \dfrac {\d^2 y} {\d x^2} + x \dfrac {\d y} {\d x} + \paren {x^2 - n^2} y = 0$

The parameter $n$ 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 $p$.

Also known as
Bessel's equation is also referred to as Bessel's differential equation.

The parameter $n$ is variously presented. Some sources use $p$.

Also see

 * Definition:Bessel's Modified Equation