JacobiND
JacobiND[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.
- 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.
Examples
open allclose allBasic Examples (4)
Scope (33)
Numerical Evaluation (4)
Specific Values (3)
Visualization (3)
Function Properties (8)
JacobiND is -periodic along the real axis:
JacobiND is -periodic along the imaginary axis:
JacobiND is an even function in its first argument:
is an analytic function of
for
:
It is not, in general, an analytic function:
It has both singularities and discontinuities:
is neither nondecreasing nor nonincreasing:
is not surjective for any fixed
:
In general, it has indeterminate sign:
JacobiND is neither convex nor concave:
Differentiation (3)
Integration (3)
Indefinite integral of JacobiND:
Definite integral of the even function over the interval centered at the origin:
Series Expansions (3)
Plot the first three approximations for around
:
Plot the first three approximations for around
:
JacobiND can be applied to a power series:
Function Identities and Simplifications (3)
Parity transformations and periodicity relations are automatically applied:
Identity involving JacobiSD:
Function Representations (3)
Applications (4)
Cartesian coordinates of a pendulum:
Plot the time‐dependence of the coordinates:
Periodic solution of the nonlinear Schrödinger equation :
Check the solution numerically:
Parametrize a lemniscate by arc length:
Show arc length parametrization and classical parametrization:
Zero modes of the periodic supersymmetric partner potentials:
Properties & Relations (2)
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Text
Wolfram Research (1988), JacobiND, Wolfram Language function, https://reference.wolfram.com/language/ref/JacobiND.html.
CMS
Wolfram Language. 1988. "JacobiND." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JacobiND.html.
APA
Wolfram Language. (1988). JacobiND. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JacobiND.html