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BUILT-IN MATHEMATICA SYMBOL
ModularLambda
ModularLambda[
]
gives the modular lambda elliptic function 
.
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- 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 
. »- For certain special arguments, ModularLambda automatically evaluates to exact values.
- ModularLambda can be evaluated to arbitrary numerical precision.
- ModularLambda automatically threads over lists.
New in 3
