Kelvin functions in R

This project is maintained by abarbour

Calculation of solutions to the Kelvin Differential Equation
using Bessel functions. This package is written for `R`

, and uses
primarily
`Bessel::BesselJ`

and `Bessel::BesselK`

to calculate
the appropriate Kelvin Functions.

*The following is taken from* http://mathworld.wolfram.com/KelvinFunctions.html

Kelvin defined the Kelvin functions bei and ber according to

```
ber_v(x) + i*bei_v(x)
= J_v(x*exp(2*pi*i/4))
= exp(v*pi*i)*J_v(x*exp(-pi*i/4))
= exp(v*pi*i/2)*I_v(x*exp(pi*i/4))
= exp(3*v*pi*i/2)*I_v(x*exp(-3*pi*i/4))
```

where J_v(x) is a Bessel function of the first kind and I_v(x)

is a modified Bessel function of the first kind. These functions satisfy the
Kelvin differential equation.

Similarly, the functions kei and ker by

```
ker_v(x) + i*kei_v(x) = exp(-v*pi*i/2)*K_v(x*exp(pi*i/4))
```

where K_v(x) is a modified Bessel function of the second kind. For the special case v=0,

```
J_0(i*sqrt(i)*x)
= J_0(sqrt(2)*(i-1)*x/2)
= ber(x) + i*bei(x)
```