# Modified Bessel Function Kn (G Dataflow)

Version:
Last Modified: January 9, 2017

Computes the modified Bessel function of the second kind.  ## x

The input argument.

Default: 0 ## n

Order of the modified Bessel function. ## error in

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

Default: No error ## Kn(x)

Value of the modified Bessel function of the second kind. ## error out

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

## Algorithm for Computing the Modified Bessel Function of the Second Kind

For the modified Bessel function of the second kind of order n, also known as the hyperbolic Bessel function of the second kind, Kn(x) is a solution of the following differential equation.

${x}^{2}\frac{{d}^{2}w}{d{x}^{2}}+x\frac{dw}{dx}-\left({x}^{2}+{v}^{2}\right)w=0$

The function is defined according to the following intervals for the input values.

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

This node supports the entire domain of this function that produces real-valued results. For any integer value of order n, the function is defined for nonnegative real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported