Definition:Hankel Function/Second Kind

Definition

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 $n$.

Also known as

The Hankel functions are also known as the Bessel functions of the third kind.

However, as there are two kinds of Hankel functions:

the Hankel function of the first kind

the Hankel function of the second kind

referring to them as Bessel functions of the third kind is a recipe for confusion.

Also see

• Definition:Hankel Function of the First Kind

• Definition:Bessel Function
  • Definition:Bessel Function of the First Kind
  • Definition:Bessel Function of the Second Kind

• Results about Hankel functions can be found here.

Source of Name

This entry was named for Hermann Hankel.

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