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DOCUMENTATION CENTER SEARCH
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>
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Built-in
Mathematica
Symbol
Elliptic Integrals and Elliptic Functions
Tutorials »
|
DedekindEta
KleinInvariantJ
WeierstrassHalfPeriods
EllipticTheta
See Also »
|
q Functions
Special Functions
More About »
ModularLambda
ModularLambda
[
]
gives the modular lambda elliptic function
.
MORE INFORMATION
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.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
Evaluate numerically:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(4)
Applications
(4)
Properties & Relations
(2)
Possible Issues
(2)
SEE ALSO
DedekindEta
KleinInvariantJ
WeierstrassHalfPeriods
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
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