DoubleFloatEllipticIntegrals

special2.spad line 1197 [edit on github]

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)

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

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

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

ellipticE : DoubleFloat -> DoubleFloat

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

ellipticE : (DoubleFloat, DoubleFloat) -> DoubleFloat

ellipticE(z, m) is the incomplete 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.