Kelvin Functions ke (G Dataflow)

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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