ModularLambda

ModularLambda[τ]

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 halfperiods .
  • 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.

Examples

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Basic Examples  (2)

Evaluate numerically:

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Scope  (4)

Applications  (4)

Properties & Relations  (2)

Possible Issues  (2)

See Also

DedekindEta  KleinInvariantJ  WeierstrassHalfPeriods  EllipticTheta

Tutorials

Introduced in 1996
(3.0)