# Kelvin Functions ke (G Dataflow)

Version:
Last Modified: January 9, 2017

Computes the complex Kelvin function of the second kind.  ## x

The input argument.

Default: 0 ## n

Order of the Kelvin 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 ## ker(x) + kei(x)i

Complex value of the Kelvin function of the second kind. ## error out

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

## Algorithm for Computing the Complex Kelvin Function of the Second Kind

The complex-valued Kelvin function of the second kind of order v is a solution of the following complex-valued differential equation.

${x}^{2}\frac{{d}^{4}w}{d{x}^{4}}+x\frac{dw}{dx}-\left(i{x}^{2}+{v}^{2}\right)w=0$

The real and imaginary parts of the Kelvin function of the second kind of order v are solutions of the following differential equation.

${x}^{4}\frac{{d}^{4}w}{d{x}^{4}}+2{x}^{3}\frac{{d}^{3}w}{d{x}^{3}}-\left(1+2{v}^{2}\right)\left({x}^{2}\frac{{d}^{2}w}{d{x}^{2}}-x\frac{dw}{dx}\right)+\left({v}^{4}-4{v}^{2}+{x}^{4}\right)w=0$

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

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

For any integer value of order n, the function is defined for positive real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported