ModularLambda

ModularLambda[] gives the modular lambda elliptic function .

Mathematical function (see Section A.3.10).

ModularLambda is defined only in the upper half of the complex plane. It is not defined for real .

The argument is the ratio of Weierstrass half-periods .

ModularLambda gives the parameter for elliptic functions in terms of according to .

ModularLambda is related to EllipticTheta by where the nome is given by .

is invariant under any combination of the modular transformations and .

See Section 3.2.11 for a discussion of argument conventions for elliptic functions.

See The Mathematica Book: Section 3.2.11.

See also: DedekindEta, KleinInvariantJ, WeierstrassHalfPeriods.

Further Examples