Definition:Bessel's Equation

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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 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.


Sources