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