Definition:Modified Bessel Function/Order

Definition

Consider Bessel's modified equation:

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

Let:

$\map {I_n} x$ denote the modified Bessel function of the first kind

$\map {K_n} x$ denote the modified Bessel function of the second kind

be the solutions of Bessel's modified equation as defined.

The parameter $n$ is known as the order of the modified Bessel function.