Keir: Complementary solution to the Kelvin differential equation...

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

Complementary solution to the Kelvin differential equation (K)

Description

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

Usage

Keir(x, ...)

## Default S3 method:
Keir(
  x,
  nu. = 0,
  nSeq. = 1,
  add.tol = TRUE,
  return.list = FALSE,
  show.scaling = FALSE,
  ...
)

Kei(...)

Ker(...)

Arguments

x	numeric; values to evaluate the complex solution at
...	additional arguments passed to BesselK or Keir
nu.	numeric; value of \nu in \mathcal{K}_\nu solutions
nSeq.	positive integer; equivalent to nSeq in BesselK
add.tol	logical; Should a fudge factor be added to prevent an error for zero-values?
return.list	logical; Should the result be a list instead of matrix?
show.scaling	logical; Should the normalization values be given as a message?

Details

Ker and Kei are wrapper functions which return the real and imaginary components of Keir,, 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/Kei.html

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

See Also

kelvin-package, Beir, BesselK

Examples

Keir(1:10)    # defaults to nu.=0, nSeq=1
Keir(1:10, nu.=2)
Keir(1:10, nSeq=2)
Keir(1:10, nSeq=2, return.list=TRUE)


# Imaginary component only
Kei(1:10)

# Real component only
Ker(1:10)

kelvin documentation built on April 14, 2025, 9:07 a.m.