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based on an earlier version of the Wolfram Language.
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gives the Jacobi elliptic function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • , where .
  • is a doubly periodic function in with periods and , where is the elliptic integral EllipticK.
  • JacobiND is a meromorphic function in both arguments.
  • For certain special arguments, JacobiND automatically evaluates to exact values.
  • JacobiND can be evaluated to arbitrary numerical precision.
  • JacobiND automatically threads over lists.
Evaluate numerically:
Series expansions about the origin:
Evaluate numerically:
Click for copyable input
Click for copyable input
Series expansions about the origin:
Click for copyable input
Click for copyable input
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
JacobiND threads element-wise over lists:
Simple exact values are generated automatically:
Parity transformations and periodicity relations are automatically applied:
TraditionalForm formatting:
JacobiND can be applied to a power series:
Cartesian coordinates of a pendulum:
Plot the time-dependence of the coordinates:
Plot the trajectory:
Periodic solution of the nonlinear Schrödinger equation :
Check the solution numerically:
Plot the solution:
Parametrize a lemniscate by arc length:
Show arc length parametrization and classical parametrization:
Zero modes of the periodic supersymmetric partner potentials:
Check the solutions:
Plot the zero modes:
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Solve a transcendental equation:
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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