ModularLambda

Usage

• ModularLambda[] gives the modular lambda elliptic function .

Notes

• 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 3.2.12 for a discussion of argument conventions for elliptic functions.

• New in Version 3.