boostmath (version 1.0.0)

elliptic_integrals: Elliptic Integrals

Description

Functions to compute various elliptic integrals, including Carlson's elliptic integrals and incomplete elliptic integrals.

Usage

ellint_rf(x, y, z)
ellint_rd(x, y, z)
ellint_rj(x, y, z, p)
ellint_rc(x, y)
ellint_rg(x, y, z)
ellint_1(k, phi = NULL)
ellint_2(k, phi = NULL)
ellint_3(k, n, phi = NULL)
ellint_d(k, phi = NULL)
jacobi_zeta(k, phi)
heuman_lambda(k, phi)

Value

A single numeric value with the computed elliptic integral.

Arguments

x

First parameter of the integral

y

Second parameter of the integral

z

Third parameter of the integral

p

Fourth parameter of the integral (for Rj)

k

Elliptic modulus (for incomplete elliptic integrals)

phi

Amplitude (for incomplete elliptic integrals)

n

Characteristic (for incomplete elliptic integrals of the third kind)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Carlson's elliptic integral Rf with parameters x = 1, y = 2, z = 3
ellint_rf(1, 2, 3)
#' # Carlson's elliptic integral Rd with parameters x = 1, y = 2, z = 3
ellint_rd(1, 2, 3)
# Carlson's elliptic integral Rj with parameters x = 1, y = 2, z = 3, p = 4
ellint_rj(1, 2, 3, 4)
# Carlson's elliptic integral Rc with parameters x = 1, y = 2
ellint_rc(1, 2)
# Carlson's elliptic integral Rg with parameters x = 1, y = 2, z = 3
ellint_rg(1, 2, 3)
# Incomplete elliptic integral of the first kind with k = 0.5, phi = pi/4
ellint_1(0.5, pi / 4)
# Complete elliptic integral of the first kind
ellint_1(0.5)
# Incomplete elliptic integral of the second kind with k = 0.5, phi = pi/4
ellint_2(0.5, pi / 4)
# Complete elliptic integral of the second kind
ellint_2(0.5)
# Incomplete elliptic integral of the third kind with k = 0.5, n = 0.5, phi = pi/4
ellint_3(0.5, 0.5, pi / 4)
# Complete elliptic integral of the third kind with k = 0.5, n = 0.5
ellint_3(0.5, 0.5)
# Incomplete elliptic integral D with k = 0.5, phi = pi/4
ellint_d(0.5, pi / 4)
# Complete elliptic integral D
ellint_d(0.5)
# Jacobi zeta function with k = 0.5, phi = pi/4
jacobi_zeta(0.5, pi / 4)
# Heuman's lambda function with k = 0.5, phi = pi/4
heuman_lambda(0.5, pi / 4)