This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# JacobiNC

 JacobiNCgives 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.
• JacobiNC is a meromorphic function in both arguments.
• For certain special arguments, JacobiNC automatically evaluates to exact values.
• JacobiNC can be evaluated to arbitrary numerical precision.
• JacobiNC automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
 Out[1]=

 Out[1]=

 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 values are generated automatically:
Parity transformations and periodicity relations are automatically applied:
JacobiNC can be applied to power series:
 Applications   (4)
Conformal map from a unit triangle to the unit disk:
Show points before and after the map:
Parametrize a lemniscate by arc length:
Show arc length parametrization and classical parametrization:
Solution of an anharmonic oscillator :
Plot various solutions:
Solution of the field theory wave equation :
Plot a 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:
New in 1