Category:Definitions/Hankel Functions

This category contains definitions related to Hankel Functions.
Related results can be found in Category:Hankel Functions.

A Hankel function is the sum of Bessel functions in either of the following two ways:

Hankel Function of the First Kind

The Hankel function of the first kind is defined as:

$\map {H_n^{\paren 1} } z = \map {J_n} z + i \map {Y_n} z$

where:

$\map {J_n} z$ denotes the Bessel function of the first kind of order $n$

$\map {Y_n} z$ denotes the Bessel function of the second kind of order $n$.

Hankel Function of the Second Kind

The Hankel function of the second kind is defined as:

$\map {H_n^{\paren 2} } z = \map {J_n} z - i \map {Y_n} z$

where:

$\map {J_n} z$ denotes the Bessel function of the first kind of order $n$

$\map {Y_n} z$ denotes the Bessel function of the second kind of order $n$.