Math.Eisenstein

Documentation

lambda

Arguments

:: Complex Double

tau

-> Complex Double

Lambda modular function (square of elliptic modulus)

eisensteinE2

Arguments

:: Complex Double

tau

-> Complex Double

Eisenstein series of weight 2

eisensteinE4

Arguments

:: Complex Double

tau

-> Complex Double

Eisenstein series of weight 4

eisensteinE6

Arguments

:: Complex Double

tau

-> Complex Double

Eisenstein series of weight 6

kleinJ

Arguments

:: Complex Double

tau

-> Complex Double

Klein J-function

kleinJinv :: Complex Double -> Complex Double

Inverse Klein-J function

modularDiscriminant

Arguments

:: Complex Double

tau

-> Complex Double

Modular discriminant

agm

Arguments

:: Complex Double

x

-> Complex Double

y

-> Complex Double

Arithmetic-geometric mean

etaDedekind

Arguments

:: Complex Double

tau

-> Complex Double

Dedekind eta function

jtheta1DashDashDash0

Arguments

:: Complex Double

tau

-> Complex Double

Third derivative at 0 of the first Jacobi theta function

jtheta1Dash

Arguments

:: Complex Double

z

-> Complex Double

q, the nome

-> Complex Double

Derivative of the first Jacobi theta function