JacobiDN

JacobiDN[u,m]

gives the Jacobi elliptic function .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • , where .
  • a is doubly periodic function in u with periods and , where is the elliptic integral EllipticK.
  • JacobiDN is a meromorphic function in both arguments.
  • For certain special arguments, JacobiDN automatically evaluates to exact values.
  • JacobiDN can be evaluated to arbitrary numerical precision.
  • JacobiDN automatically threads over lists.

Examples

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Basic Examples  (3)

Evaluate numerically:

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Series expansions about the origin:

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Scope  (6)

Generalizations & Extensions  (1)

Applications  (8)

Properties & Relations  (4)

Possible Issues  (2)

See Also

InverseJacobiDN  JacobiDC  JacobiDS

Tutorials

Introduced in 1988
(1.0)