# DoubleFloatEllipticIntegralsΒΆ

`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`.