# Hankel Function Hv (G Dataflow)

Last Modified: June 25, 2019

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

Input argument.

This input accepts a double-precision, floating-point number or a complex double-precision, floating-point number.

Default: The default value is 0 if x is a double-precision, floating-point number. The default value is 0 + 0i if x is a complex double-precision, floating-point number. ## 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.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## Hv(x)

Value of the Hankel function. ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## 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

Web Server: Not supported in VIs that run in a web application