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Type: Package
Title: Carlson Elliptic Integrals and Incomplete Elliptic Integrals
Version: 3.0.0
Date: 2023-11-10
Author: Stéphane Laurent
Maintainer: Stéphane Laurent <laurent_step@outlook.fr>
Description: Evaluation of the Carlson elliptic integrals and the incomplete elliptic integrals with complex arguments. The implementations use Carlson's algorithms <doi:10.1007/BF02198293>. Applications of elliptic integrals include probability distributions, geometry, physics, mechanics, electrodynamics, statistical mechanics, astronomy, geodesy, geodesics on conics, and magnetic field calculations.
License: GPL-3
URL: https://github.com/stla/Carlson
BugReports: https://github.com/stla/Carlson/issues
Imports: Rcpp
LinkingTo: Rcpp
Suggests: gsl, testthat
Encoding: UTF-8
RoxygenNote: 7.2.3
NeedsCompilation: yes
Packaged: 2023-11-10 17:00:11 UTC; SDL96354
Repository: CRAN
Date/Publication: 2023-11-10 19:33:25 UTC

Carlson elliptic integral RC

Description

Evaluate the Carlson elliptic integral RC.

Usage

Carlson_RC(x, y, minerror = 1e-15)

Arguments

x, y

real or complex numbers, with y different from 0

minerror

bound on the relative error passed to Carlson_RF

Value

A complex number, the value of the Carlson elliptic integral RC(x,y).

Note

The function returns a value when x or y are negative real numbers, but this value is not the one of the Carlson integral.

Examples

Carlson_RC(5, 2)
gsl::ellint_RC(5, 2)

Carlson elliptic integral RD

Description

Evaluate the Carlson elliptic integral RD.

Usage

Carlson_RD(x, y, z, minerror = 1e-15)

Arguments

x, y, z

real or complex numbers; at most one can be 0

minerror

bound on the relative error

Value

A complex number, the value of the Carlson elliptic integral RD(x,y,z).

Note

The function returns a value when x, y or z are negative real numbers, but this value is not the one of the Carlson integral.

Examples

Carlson_RD(5, 2, 3)
gsl::ellint_RD(5, 2, 3)

Carlson elliptic integral RF

Description

Evaluate the Carlson elliptic integral RF.

Usage

Carlson_RF(x, y, z, minerror = 1e-15)

Arguments

x, y, z

real or complex numbers; at most one can be 0

minerror

bound on relative error

Value

A complex number, the value of the Carlson elliptic integral RF(x,y,z).

Note

The function returns a value when x, y or z are negative real numbers, but this value is not the one of the Carlson integral.

Examples

Carlson_RF(5, 2, 3)
gsl::ellint_RF(5, 2, 3)

Carlson elliptic integral RG

Description

Evaluate the Carlson elliptic integral RG.

Usage

Carlson_RG(x, y, z, minerror = 1e-15)

Arguments

x, y, z

real or complex numbers; they can be zero

minerror

bound on the relative error passed to Carlson_RF and Carlson_RD

Value

A complex number, the value of the Carlson elliptic integral RG(x,y,z).


Carlson elliptic integral RJ

Description

Evaluate the Carlson elliptic integral RJ.

Usage

Carlson_RJ(x, y, z, p, minerror = 1e-15)

Arguments

x, y, z, p

real or complex numbers; at most one can be 0

minerror

bound on the relative error

Value

A complex number, the value of the Carlson elliptic integral RJ(x,y,z,t).

Note

The function returns a value when x, y, z or p are negative real numbers, but this value is not the one of the Carlson integral.

Examples

Carlson_RJ(5, 2, 3, 4)
gsl::ellint_RJ(5, 2, 3, 4)

Heuman Lambda function

Description

Evaluates the Heuman Lambda function.

Usage

Lambda0(phi, m, minerror = 1e-14)

Arguments

phi

Jacobi amplitude, a complex number/vector

m

parameter, a complex number/vector

minerror

the bound on the relative error passed to elliptic_F and elliptic_Z

Value

A complex number or vector.


Incomplete elliptic integral of the second kind

Description

Evaluate the incomplete elliptic integral of the second kind.

Usage

elliptic_E(phi, m, minerror = 1e-15)

Arguments

phi

amplitude, real or complex number/vector

m

parameter, real or complex number/vector

minerror

the bound on the relative error passed to Carlson_RF and Carlson_RD

Value

A complex number or vector, the value(s) of the incomplete elliptic integral E(φ,m).

Examples

elliptic_E(1, 0.2)
gsl::ellint_E(1, sqrt(0.2))

Incomplete elliptic integral of the first kind

Description

Evaluate the incomplete elliptic integral of the first kind.

Usage

elliptic_F(phi, m, minerror = 1e-15)

Arguments

phi

amplitude, real or complex number/vector

m

parameter, real or complex number/vectot

minerror

the bound on the relative error passed to Carlson_RF

Value

A complex number or vector, the value(s) of the incomplete elliptic integral F(φ,m).

Examples

elliptic_F(1, 0.2)
gsl::ellint_F(1, sqrt(0.2))

Incomplete elliptic integral of the third kind

Description

Evaluate the incomplete elliptic integral of the third kind.

Usage

elliptic_PI(phi, n, m, minerror = 1e-15)

Arguments

phi

amplitude, real or complex number/vector

n

characteristic, real or complex number/vector

m

parameter, real or complex number/vector

minerror

the bound on the relative error passed to Carlson_RF and Carlson_RJ

Value

A complex number or vector, the value(s) of the incomplete elliptic integral Π(φ,n,m).

Examples

elliptic_PI(1, 0.8, 0.2)
gsl::ellint_P(1, sqrt(0.2), -0.8)

Jacobi zeta function

Description

Evaluate the Jacobi zeta function.

Usage

elliptic_Z(phi, m, minerror = 1e-15)

Arguments

phi

amplitude, real or complex number/vector

m

parameter, real or complex number/vector

minerror

bound on relative error passed to elliptic_E and elliptic_F

Value

A complex number or vector, the value(s) of the Jacobi zeta function Z(φ,m).

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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