This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# JacobiCS

 JacobiCSgives the Jacobi elliptic function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• , where .
• is a doubly periodic function in u with periods and , where is the elliptic integral EllipticK.
• JacobiCS is a meromorphic function in both arguments.
• For certain special arguments, JacobiCS automatically evaluates to exact values.
• JacobiCS can be evaluated to arbitrary numerical precision.
• JacobiCS automatically threads over lists.
Evaluate numerically:
Series expansions:
Evaluate numerically:
 Out[1]=

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Series expansions:
 Out[1]=
 Out[2]=
 Scope   (6)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact results are generated automatically:
Parity transformation and periodicity relations are automatically applied:
JacobiCS can be applied to a power series:
 Applications   (4)
Hierarchy of solutions of the nonlinear diffusion equation :
Check:
Flow lines in a rectangular region with a current flowing from the lower-right to the upper-left corner:
Conformal map from a unit triangle to the unit disk:
Show points before and after the map:
Solution of the sinh-Gordon equation :
Check the solution:
Plot the solution:
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Solve a transcendental equation:
Integrals:
Machine-precision input is insufficient to give the correct answer:
Currently only simple simplification rules are built in for Jacobi functions:
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