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

- 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.
- JacobiDS is a meromorphic function in both arguments.
- For certain special arguments, JacobiDS automatically evaluates to exact values.
- JacobiDS can be evaluated to arbitrary numerical precision.
- JacobiDS 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)
Integration (3)
Indefinite integral of JacobiDS:
Definite integral of an odd function over the interval centered at the origin is 0:
Series Expansions (3)
Plot the first three approximations for around
:
Plot the first three approximations for around
:
JacobiDS can be applied to a power series:
Function Identities and Simplifications (3)
Parity transformation and periodicity relations are automatically applied:
Identity involving JacobiCS:
Function Representations (3)
Representation in terms of Csc 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), JacobiDS, Wolfram Language function, https://reference.wolfram.com/language/ref/JacobiDS.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "JacobiDS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JacobiDS.html.
APA
Wolfram Language. (1988). JacobiDS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JacobiDS.html