Definition:Bessel's Modified Equation

Equation
Bessel's modified 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 modified equation with parameter $n$ are known as modified Bessel functions of order $n$, and they are functions of the parameter $n$.

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

Some sources present it as the modified Bessel equation.

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

Also see

 * Definition:Bessel's Equation