| 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 |
minerror |
bound on the relative error passed to |
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
|
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
|
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
|
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
|
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
|
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 |
Value
A complex number or vector, the value(s) of the Jacobi zeta function Z(φ,m).