JacobiNS
JacobiNS[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.
- JacobiNS is a meromorphic function in both arguments.
- For certain special arguments, JacobiNS automatically evaluates to exact values.
- JacobiNS can be evaluated to arbitrary numerical precision.
- JacobiNS automatically threads over lists.
Examples
open allclose allBasic Examples (4)
Scope (33)
Numerical Evaluation (4)
Specific Values (3)
Visualization (3)
Function Properties (8)
JacobiNS is -periodic along the real axis:
JacobiNS is -periodic along the imaginary axis:
JacobiNS is an odd function in its first argument:
JacobiNS is not an analytic function:
It has both singularities and discontinuities:
is neither nondecreasing nor nonincreasing:
is not injective for any fixed
:
JacobiNS is not surjective for any fixed :
JacobiNS is neither non-negative nor non-positive:
JacobiNS is neither convex nor concave:
Differentiation (3)
Integration (3)
Indefinite integral of JacobiNS:
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
:
JacobiNS can be applied to 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 (5)
Properties & Relations (2)
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Text
Wolfram Research (1988), JacobiNS, Wolfram Language function, https://reference.wolfram.com/language/ref/JacobiNS.html.
CMS
Wolfram Language. 1988. "JacobiNS." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JacobiNS.html.
APA
Wolfram Language. (1988). JacobiNS. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JacobiNS.html