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DOCUMENTATION CENTER SEARCH
Mathematica
>
Mathematics and Algorithms
>
Mathematical Functions
>
Special Functions
>
Elliptic Integrals
>
Built-in
Mathematica
Symbol
Elliptic Integrals and Elliptic Functions
Tutorials »
|
EllipticK
EllipticE
EllipticPi
JacobiZeta
JacobiAmplitude
See Also »
|
Elliptic Integrals
Special Functions
More About »
EllipticF
EllipticF
[
,
m
]
gives the elliptic integral of the first kind
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
For
,
.
The complete elliptic integral associated with
EllipticF
is
EllipticK
.
EllipticF
is the inverse of
JacobiAmplitude
. If
then
.
EllipticF
[
,
m
]
has a branch cut discontinuity running along the ray from
to infinity.
For certain special arguments,
EllipticF
automatically evaluates to exact values.
EllipticF
can be evaluated to arbitrary numerical precision.
EllipticF
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
In[1]:=
Out[1]=
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(7)
Generalizations & Extensions
(1)
Applications
(5)
Properties & Relations
(6)
Possible Issues
(3)
Neat Examples
(2)
SEE ALSO
EllipticK
EllipticE
EllipticPi
JacobiZeta
JacobiAmplitude
TUTORIALS
Elliptic Integrals and Elliptic Functions
RELATED LINKS
MathWorld
The Wolfram Functions Site
MORE ABOUT
Elliptic Integrals
Special Functions
New in 1 | Last modified in 3
, m]
. 
, 
. 
then 
. , m] has a branch cut discontinuity running along the ray from 
to infinity.
EXAMPLES
Basic Examples 
Scope 