Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate JacobiCD efficiently at high precision:

JacobiCD threads elementwise over lists:

Simple exact answers are generated automatically:

Some poles of JacobiCD:

Find a zero of :

Plot the JacobiCD functions for various values of parameter:

Plot JacobiCD as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

JacobiCD is -periodic along the real axis:

JacobiCD is -periodic along the imaginary axis:

JacobiCD 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 for :

is neither nondecreasing nor nonincreasing:

is not injective for any fixed :

is not surjective for any fixed :

JacobiCD is neither non-negative nor non-positive:

JacobiCD is neither convex nor concave:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Derivative with respect to :

Indefinite integral of JacobiCD:

Definite integral of an even integrand over the interval centered at the origin:

This is twice the integral over half the interval:

More integrals:

Taylor expansion for :

Plot the first three approximations for around :

Taylor expansion for :

Plot the first three approximations for around :

JacobiCD can be applied to a power series:

Primary definition:

Parity transformations and periodicity relations are automatically applied:

Automatic argument simplifications:

Representation in terms of trigonometry functions and JacobiAmplitude:

Relation to other Jacobi elliptic functions:

TraditionalForm formatting: