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JacobiNC

JacobiNC
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.
  • 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:
Series expansions about the origin:
Evaluate numerically:
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Series expansions about the origin:
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Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
JacobiNC threads element-wise over lists:
Simple exact values are generated automatically:
Parity transformations and periodicity relations are automatically applied:
TraditionalForm formatting:
JacobiNC can be applied to power series:
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:
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