JacobiCN

Evaluate for complex arguments:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

JacobiCN threads element-wise over lists:

Simple exact values are generated automatically:

Parity transformations and periodicity relations are automatically applied:

TraditionalForm formatting:

JacobiCN can be applied to power series:

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: