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JacobiSN
JacobiSN
[
u
,
m
]
gives the Jacobi elliptic function
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
, where
.
is a doubly periodic function in
with periods
and
, where
is the elliptic integral
EllipticK
.
JacobiSN
is a meromorphic function in both arguments.
For certain special arguments,
JacobiSN
automatically evaluates to exact values.
JacobiSN
can be evaluated to arbitrary numerical precision.
JacobiSN
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Evaluate numerically:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Series expansions about the origin:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Scope
(5)
Generalizations & Extensions
(1)
Applications
(7)
Properties & Relations
(6)
Possible Issues
(2)
SEE ALSO
InverseJacobiSN
JacobiAmplitude
JacobiSC
JacobiSD
TUTORIALS
Elliptic Integrals and Elliptic Functions
MORE ABOUT
Elliptic Functions
Mathematical Functions
Special Functions
RELATED LINKS
NKS|Online
(
A New Kind of Science
)
New in 1
© 2008 Wolfram Research, Inc.
.
, where 
. 
is a doubly periodic function in 
with periods 
and 
, where 
is the elliptic integral EllipticK.
EXAMPLES
Basic Examples 
Scope 