Beir: Fundamental solution to the Kelvin differential equation (J)

In kelvin: Calculate Solutions to the Kelvin Differential Equation using Bessel Functions

Fundamental solution to the Kelvin differential equation (J)

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

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 \nu in \mathcal{B}_\nu 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.

Author(s)

Andrew Barbour

References

https://mathworld.wolfram.com/KelvinFunctions.html

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

Real: https://mathworld.wolfram.com/Ber.html

See Also

kelvin-package, Keir, BesselJ

Examples

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 April 14, 2025, 9:07 a.m.