| Title: | Carlson Elliptic Integrals and Incomplete Elliptic Integrals |
|---|---|
| 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. |
| Authors: | Stéphane Laurent |
| Maintainer: | Stéphane Laurent <[email protected]> |
| License: | GPL-3 |
| Version: | 3.0.0 |
| Built: | 2024-11-04 02:47:31 UTC |
| Source: | https://github.com/stla/carlson |
Evaluate the Carlson elliptic integral RC.
Carlson_RC(x, y, minerror = 1e-15)Carlson_RC(x, y, minerror = 1e-15)
x, y
|
real or complex numbers, with |
minerror |
bound on the relative error passed to |
A complex number, the value of the Carlson elliptic integral RC(x,y).
The function returns a value when x or y
are negative real numbers, but this value is not the one of the
Carlson integral.
Carlson_RC(5, 2) gsl::ellint_RC(5, 2)Carlson_RC(5, 2) gsl::ellint_RC(5, 2)
Evaluate the Carlson elliptic integral RD.
Carlson_RD(x, y, z, minerror = 1e-15)Carlson_RD(x, y, z, minerror = 1e-15)
x, y, z
|
real or complex numbers; at most one can be 0 |
minerror |
bound on the relative error |
A complex number, the value of the Carlson elliptic integral RD(x,y,z).
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.
Carlson_RD(5, 2, 3) gsl::ellint_RD(5, 2, 3)Carlson_RD(5, 2, 3) gsl::ellint_RD(5, 2, 3)
Evaluate the Carlson elliptic integral RF.
Carlson_RF(x, y, z, minerror = 1e-15)Carlson_RF(x, y, z, minerror = 1e-15)
x, y, z
|
real or complex numbers; at most one can be 0 |
minerror |
bound on relative error |
A complex number, the value of the Carlson elliptic integral RF(x,y,z).
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.
Carlson_RF(5, 2, 3) gsl::ellint_RF(5, 2, 3)Carlson_RF(5, 2, 3) gsl::ellint_RF(5, 2, 3)
Evaluate the Carlson elliptic integral RG.
Carlson_RG(x, y, z, minerror = 1e-15)Carlson_RG(x, y, z, minerror = 1e-15)
x, y, z
|
real or complex numbers; they can be zero |
minerror |
bound on the relative error passed to
|
A complex number, the value of the Carlson elliptic integral RG(x,y,z).
Evaluate the Carlson elliptic integral RJ.
Carlson_RJ(x, y, z, p, minerror = 1e-15)Carlson_RJ(x, y, z, p, minerror = 1e-15)
x, y, z, p
|
real or complex numbers; at most one can be 0 |
minerror |
bound on the relative error |
A complex number, the value of the Carlson elliptic integral RJ(x,y,z,t).
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.
Carlson_RJ(5, 2, 3, 4) gsl::ellint_RJ(5, 2, 3, 4)Carlson_RJ(5, 2, 3, 4) gsl::ellint_RJ(5, 2, 3, 4)
Evaluate the incomplete elliptic integral of the second kind.
elliptic_E(phi, m, minerror = 1e-15)elliptic_E(phi, m, minerror = 1e-15)
phi |
amplitude, real or complex number/vector |
m |
parameter, real or complex number/vector |
minerror |
the bound on the relative error passed to
|
A complex number or vector, the value(s) of the incomplete elliptic integral E(φ,m).
elliptic_E(1, 0.2) gsl::ellint_E(1, sqrt(0.2))elliptic_E(1, 0.2) gsl::ellint_E(1, sqrt(0.2))
Evaluate the incomplete elliptic integral of the first kind.
elliptic_F(phi, m, minerror = 1e-15)elliptic_F(phi, m, minerror = 1e-15)
phi |
amplitude, real or complex number/vector |
m |
parameter, real or complex number/vectot |
minerror |
the bound on the relative error passed to
|
A complex number or vector, the value(s) of the incomplete elliptic integral F(φ,m).
elliptic_F(1, 0.2) gsl::ellint_F(1, sqrt(0.2))elliptic_F(1, 0.2) gsl::ellint_F(1, sqrt(0.2))
Evaluate the incomplete elliptic integral of the third kind.
elliptic_PI(phi, n, m, minerror = 1e-15)elliptic_PI(phi, n, m, minerror = 1e-15)
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
|
A complex number or vector, the value(s) of the incomplete elliptic integral Π(φ,n,m).
elliptic_PI(1, 0.8, 0.2) gsl::ellint_P(1, sqrt(0.2), -0.8)elliptic_PI(1, 0.8, 0.2) gsl::ellint_P(1, sqrt(0.2), -0.8)
Evaluate the Jacobi zeta function.
elliptic_Z(phi, m, minerror = 1e-15)elliptic_Z(phi, m, minerror = 1e-15)
phi |
amplitude, real or complex number/vector |
m |
parameter, real or complex number/vector |
minerror |
bound on relative error passed to |
A complex number or vector, the value(s) of the Jacobi zeta function Z(φ,m).
Evaluates the Heuman Lambda function.
Lambda0(phi, m, minerror = 1e-14)Lambda0(phi, m, minerror = 1e-14)
phi |
Jacobi amplitude, a complex number/vector |
m |
parameter, a complex number/vector |
minerror |
the bound on the relative error passed to
|
A complex number or vector.