# 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.