DoubleFloatEllipticIntegrals¶

DoubleFloatEllipticIntegrals implements machine A package for computing machine precision real and complex elliptic integrals, using algorithms given by Carlson. Note: Complex versions may misbehave for very large/small arguments and close to branch cuts.

ellipticE: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticE(z, m) is the incomplete elliptic integral of the second kind.

ellipticE: (DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticE(z, m) is the incomplete elliptic integral of the second kind.

ellipticE: Complex DoubleFloat -> Complex DoubleFloat

ellipticE(m) is the complete elliptic integral of the second kind

ellipticE: DoubleFloat -> DoubleFloat

ellipticE(m) is the complete elliptic integral of the second kind

ellipticF: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticF(z, m) is the incomplete elliptic integral of the first kind.

ellipticF: (DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticF(z, m) is the incomplete elliptic integral of the first kind.

ellipticK: Complex DoubleFloat -> Complex DoubleFloat

ellipticK(z, m) is the incomplete elliptic integral of the first kind.

ellipticK: DoubleFloat -> DoubleFloat

ellipticK(z, m) is the complete elliptic integral of the first kind.

ellipticPi: (Complex DoubleFloat, Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticPi(z, n, m) is the incomplete elliptic integral of the third kind.

ellipticPi: (DoubleFloat, DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticPi(z, n, m) is the incomplete elliptic integral of the third kind.

ellipticRC: (Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticRC(x, y) computes integral from 0 to infinity of (1/2)*(t+x)^(-1/2)*(t+y)^(-1)dt.

ellipticRC: (DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticRC(x, y) computes integral from 0 to infinity of (1/2)*(t+x)^(-1/2)*(t+y)^(-1)dt.

ellipticRD: (Complex DoubleFloat, Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticRD(x, y, z) computes integral from 0 to infinity of (3/2)*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+Z)^(-3/2)dt.

ellipticRD: (DoubleFloat, DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticRD(x, y, z) computes integral from 0 to infinity of (3/2)*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+Z)^(-3/2)dt.

ellipticRF: (Complex DoubleFloat, Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticRF(x, y, z) computes integral from 0 to infinity of (1/2)*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+Z)^(-1/2)dt.

ellipticRF: (DoubleFloat, DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticRF(x, y, z) computes integral from 0 to infinity of (1/2)*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+Z)^(-1/2)dt.

ellipticRJ: (Complex DoubleFloat, Complex DoubleFloat, Complex DoubleFloat, Complex DoubleFloat) -> Complex DoubleFloat

ellipticRF(x, y, z, p) computes integral from 0 to infinity of (3/2)*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+Z)^(-1/2)*(t+p)^(-1)dt.

ellipticRJ: (DoubleFloat, DoubleFloat, DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticRJ(x, y, z, p) computes integral from 0 to infinity of (3/2)*(t+x)^(-1/2)*(t+y)^(-1/2)*(t+Z)^(-1/2)*(t+p)^(-1)dt.