# Hankel Function Hv (G Dataflow)

Version:

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

## x

The input argument.

Default: 0

## v

Order of the Hankel function.

## type

Type of the Hankel function.

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

## Hv(x)

Value of the Hankel function.

## error out

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

## Algorithm for Computing the Hankel Function

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

${H}_{v}^{\left(1\right)}\left(x\right)={J}_{v}\left(x\right)+i{Y}_{v}\left(x\right)$

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

${H}_{v}^{\left(2\right)}\left(x\right)={J}_{v}\left(x\right)-i{Y}_{v}\left(x\right)$

where Jv is a Bessel function of the first kind and Yv is a Bessel function of the second kind.

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

$v\in \Re ,x\in \left(0,\infty \right)$

For any real value of order v, this node supports positive real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported