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KleinInvariantJ
KleinInvariantJ
[
]
gives the Klein invariant modular elliptic function
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
The argument
is the ratio of Weierstrass half-periods
.
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:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(4)
Applications
(6)
Properties & Relations
(2)
Possible Issues
(2)
SEE ALSO
ModularLambda
DedekindEta
WeierstrassInvariants
EllipticTheta
TUTORIALS
Elliptic Integrals and Elliptic Functions
RELATED LINKS
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
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