# Spherical Hankel Function hn (G Dataflow)

Version:

Computes the spherical Hankel function, which is also known as the spherical Bessel function of the third kind.

## x

The input argument.

Default: 0

## n

Order of the spherical Hankel function.

## type

Type of the spherical Hankel function.

Name Value Description
0 0 Computes the spherical Hankel function of the first kind.
1 1 Computes the spherical Hankel function of the second kind.

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## hn(x)

Value of the spherical Hankel function.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Computing the Spherical Hankel Function

The following equation defines the spherical Hankel function of the first kind of order n.

${{h}_{n}}^{\left(1\right)}\left(x\right)={j}_{n}\left(x\right)+i{y}_{n}\left(x\right)$

The following equation defines the spherical Hankel function of the second kind of order n.

${{h}_{n}}^{\left(2\right)}\left(x\right)={j}_{n}\left(x\right)-i{y}_{n}\left(x\right)$

where jn is a spherical Bessel function of the first kind and yn is a spherical Bessel function of the second kind.

The following intervals for the input values of the node define the spherical Hankel function.

$n\in \Im ,x\in \left[0,\infty \right)$

For any integer value of order n, this node supports nonnegative real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported