JacobiNC
JacobiNC[u,m]
gives the Jacobi elliptic function .
Details

- 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.
Examples
open allclose allBasic Examples (4)
Scope (27)
Numerical Evaluation (4)
Specific Values (3)
Visualization (3)
Function Properties (2)
Differentiation (3)
Series Expansions (3)
Plot the first three approximations for around
:
Plot the first three approximations for around
:
JacobiNC can be applied to power series:
Function Identities and Simplifications (3)
Parity transformations and periodicity relations are automatically applied:
Identity involving JacobiSC:
Function Representations (3)
Representation in terms of Sec of JacobiAmplitude:
Relation to other Jacobi elliptic functions:
TraditionalForm formatting:
Applications (4)
Properties & Relations (2)
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Text
Wolfram Research (1988), JacobiNC, Wolfram Language function, https://reference.wolfram.com/language/ref/JacobiNC.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "JacobiNC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JacobiNC.html.
APA
Wolfram Language. (1988). JacobiNC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JacobiNC.html