# Beir: Fundamental solution to the Kelvin differential equation (J) In kelvin: Calculate Solutions to the Kelvin Differential Equation using Bessel Functions

## Description

This function calculates the complex solution to the Kelvin differential equation using modified Bessel functions of the first kind, specifically those produced by `BesselJ`.

## Usage

 ```1 2 3 4 5 6 7 8``` ```Beir(x, ...) ## Default S3 method: Beir(x, nu. = 0, nSeq. = 1, return.list = FALSE, ...) Bei(...) Ber(...) ```

## Arguments

 `x` numeric; values to evaluate the complex solution at `...` additional arguments passed to `BesselK` or `Beir` `nu.` numeric; value of ν in Bei,Ber solutions `nSeq.` positive integer; equivalent to `nSeq` in `BesselJ` `return.list` logical; Should the result be a list instead of matrix?

## Details

`Ber` and `Bei` are wrapper functions which return the real and imaginary components of `Beir`, respectively.

## Value

If `return.list==FALSE` (the default), a complex matrix with as many columns as using `nSeq.` creates. Otherwise the result is a list with matrices for Real and Imaginary components.

Andrew Barbour

## References

Imaginary: http://mathworld.wolfram.com/Bei.html

## See Also

`kelvin-package`, `Keir`, `BesselJ`

## Examples

 ```1 2 3 4 5 6 7 8``` ```Beir(1:10) # defaults to nu.=0 Beir(1:10, nu.=2) Beir(1:10, nSeq.=2) Beir(1:10, nSeq.=2, return.list=TRUE) # Imaginary component only Bei(1:10) # Real component only Ber(1:10) ```

kelvin documentation built on May 2, 2019, 3:38 p.m.