JacobiCD
JacobiCD[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.
- JacobiCD is a meromorphic function in both arguments.
- For certain special arguments, JacobiCD automatically evaluates to exact values.
- JacobiCD can be evaluated to arbitrary numerical precision.
- JacobiCD 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 JacobiCD:
Definite integral of an even integrand over the interval centered at the origin:
Series Expansions (3)
Plot the first three approximations for around
:
Plot the first three approximations for around
:
JacobiCD can be applied to a power series:
Function Identities and Simplifications (3)
Function Representations (3)
Representation in terms of trigonometry functions and JacobiAmplitude:
Relation to other Jacobi elliptic functions:
TraditionalForm formatting:
Applications (3)
Conformal map from a unit triangle to the unit disk:
Show points before and after the map:
Solution of the Poisson–Boltzmann equation :
Check solution using series expansion:
Construct lowpass elliptic filter for analog signal:
Compute filter ripple parameters and associate elliptic function parameter:
Use elliptic degree equation to find the ratio of the pass and the stop frequencies:
Compute corresponding stop frequency and elliptic parameters:
Compute ripple locations and poles and zeros of the transfer function:
Compute poles of the transfer function:
Assemble the transfer function:
Compare with the result of EllipticFilterModel:
Properties & Relations (3)
Compose with inverse functions:
Use PowerExpand to disregard multivaluedness of the inverse function:
Solve a transcendental equation:

Text
Wolfram Research (1988), JacobiCD, Wolfram Language function, https://reference.wolfram.com/language/ref/JacobiCD.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "JacobiCD." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JacobiCD.html.
APA
Wolfram Language. (1988). JacobiCD. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JacobiCD.html