# 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 with parameter $n$ are known as Bessel functions of order $n$, and they are functions of the parameter $n$.

## Also presented as

Some sources give Bessel's equation as:

$x^2 \dfrac {\d^2 y} {\d x^2} + x \dfrac {\d y} {\d x} + \paren {\lambda^2 x^2 - n^2} y = 0$

## 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

• Results about Bessel's equations can be found here.

## Source of Name

This entry was named for Friedrich Wilhelm Bessel.