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Built-in
Mathematica
Symbol
Elliptic Integrals and Elliptic Functions
Tutorials »
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ModularLambda
DedekindEta
WeierstrassInvariants
EllipticTheta
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q Functions
Special Functions
More About »
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
CLOSE ALL
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
)
MORE ABOUT
q Functions
Special Functions
New in 3
]
. 
is the ratio of Weierstrass half-periods 
. 
. 
is invariant under any combination of the modular transformations 
and 
.
EXAMPLES
Basic Examples 
Scope 