KleinInvariantJ

KleinInvariantJ[τ]

gives the Klein invariant modular elliptic function .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The argument is the ratio of Weierstrass halfperiods .
  • KleinInvariantJ is given in terms of Weierstrass invariants by .
  • is invariant under any combination of the modular transformations and .
  • For certain special arguments, KleinInvariantJ automatically evaluates to exact values.
  • KleinInvariantJ can be evaluated to arbitrary numerical precision.
  • KleinInvariantJ automatically threads over lists.

Examples

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Basic Examples  (2)

Evaluate numerically:

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Scope  (4)

Applications  (6)

Properties & Relations  (2)

Possible Issues  (2)

See Also

ModularLambda  DedekindEta  WeierstrassInvariants  EllipticTheta

Tutorials

Introduced in 1996
(3.0)