Definition:Bessel Function/Order

Definition

Consider Bessel's equation:

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

Let:

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

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

be the solutions of Bessel's equation as defined.

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

Also known as

Some sources use $p$ to denote the order of the Bessel function.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Bessel functions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Bessel functions