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# JacobiCN

 JacobiCN[u, m]gives 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.
• JacobiCN is a meromorphic function in both arguments.
• For certain special arguments, JacobiCN automatically evaluates to exact values.
• JacobiCN can be evaluated to arbitrary numerical precision.
• JacobiCN automatically threads over lists.
Evaluate numerically:
 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:
JacobiCN can be applied to power series:
 Applications   (6)
Cnoidal solution of the KdV equation:
Verify the solution:
Plot the solution:
Conformal map from a unit triangle to the unit disk:
Show points before and after the map:
Solution of an anharmonic oscillator :
Plot various solutions:
Elliptic parametrization of an ellipse:
Plot using elliptic parametrization and circular parametrization:
Solution of Nahm equations:
Check that the solutions fulfill the Nahm equations:
Parametrization of a mylar balloon (two flat sheets of plastic sewn together at their circumference and then inflated):
Plot the inflated balloon:
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Evaluate as a result of applying Cos to JacobiAmplitude:
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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