FloatEllipticFunctions

special2.spad line 2080 [edit on github]

This package implements arbitrary precision numerical elliptic functions. The method is based on descending Landen transform.

ellipticE : Complex(Float) -> Complex(Float)

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

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

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

ellipticE : Float -> Float

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

ellipticE : (Float, Float) -> Float

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

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

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

ellipticF : (Float, Float) -> Float

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

ellipticK : Complex(Float) -> Complex(Float)

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

ellipticK : Float -> Float

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

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

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

ellipticPi : (Float, Float, Float) -> Float

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

jacobiCn : (Complex(Float), Complex(Float)) -> Complex(Float)

jacobiCn(z, m) is the Jacobi cn function

jacobiCn : (Float, Float) -> Float

jacobiCn(z, m) is the Jacobi cn function

jacobiDn : (Complex(Float), Complex(Float)) -> Complex(Float)

jacobiDn(z, m) is the Jacobi dn function

jacobiDn : (Float, Float) -> Float

jacobiDn(z, m) is the Jacobi dn function

jacobiSn : (Complex(Float), Complex(Float)) -> Complex(Float)

jacobiSn(z, m) is the Jacobi sn function

jacobiSn : (Float, Float) -> Float

jacobiSn(z, m) is the Jacobi sn function

jacobiZeta : (Float, Float) -> Float

jacobiZeta(z, m) is the Jacobi zeta function

kprod : List(Complex(Float)) -> Complex(Float)

Undocumented.

kprod : List(Float) -> Float

Undocumented.

landen : (Complex(Float), Float) -> List(Complex(Float))

Undocumented.

landen : (Float, Float) -> List(Float)

Undocumented.

landen1 : (Complex(Float), List(Complex(Float))) -> List(Complex(Float))

Undocumented.

landen1 : (Float, List(Float)) -> List(Float)

Undocumented.

landen2 : (Complex(Float), List(Complex(Float)), Float) -> List(Complex(Float))

Undocumented.

landen2 : (Float, List(Float), Float) -> List(Float)

Undocumented.

modularInvariantJ : Complex(Float) -> Complex(Float)

modularInvariantJ(tau) computes modular invariant j, that is 1728*g2^3/(g2^3 - 27*g3^2) where g2, g3 are invariants corresponding to half periods w1, w2 such that tau = w1/w2.

rabs : Complex(Float) -> Float

Undocumented.

rabs : Float -> Float

Undocumented.

sn2 : (Complex(Float), List(Complex(Float))) -> Complex(Float)

Undocumented.

sn2 : (Float, List(Float)) -> Float

Undocumented.

weierstrassHalfPeriods : (Complex(Float), Complex(Float)) -> List(Complex(Float))

weierstrassHalfPeriods(g2, g3) computes half periods of Weierstrass elliptic functions from invariants g2, g3.

weierstrassInvariants : (Complex(Float), Complex(Float)) -> List(Complex(Float))

weierstrassInvariants(w1, w2) computes invariants g2, g3 of Weierstrass elliptic functions from half periods w1, w2.

weierstrassP : (Complex(Float), Complex(Float), Complex(Float)) -> Complex(Float)

weierstrassP(g2, g3, x) is the Weierstrass P function

weierstrassP : (Float, Float, Float) -> Float

weierstrassP(g2, g3, x) is the Weierstrass P function

weierstrassPPrime : (Complex(Float), Complex(Float), Complex(Float)) -> Complex(Float)

weierstrassPPrime(g2, g3, x) is the derivative of the Weierstrass P function

weierstrassPPrime : (Float, Float, Float) -> Float

weierstrassPPrime(g2, g3, x) is the derivative of the Weierstrass P function