Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate JacobiDC efficiently at high precision:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix JacobiDC function using MatrixFunction:

Simple exact answers are generated automatically:

Some poles of JacobiDC:

Find a local maximum of JacobiDC as a root of :

Plot the JacobiDC functions for various parameter values:

Plot JacobiDC as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

JacobiDC is -periodic along the real axis:

JacobiDC is -periodic along the imaginary axis:

JacobiDC is an even function:

is an analytic function of for :

It is not, in general, analytic:

It has both singularities and discontinuities for :

is neither nondecreasing nor nonincreasing:

is not injective for any fixed :

is not surjective for any fixed :

JacobiDC is neither non-negative nor non-positive:

JacobiDC is neither convex nor concave:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Derivative with respect to :

Indefinite integral of JacobiDC:

Definite integral of JacobiDC:

More integrals:

Taylor expansion for :

Plot the first three approximations for around :

Taylor expansion for :

Plot the first three approximations for around :

JacobiDC can be applied to a power series:

Primary definition:

Identity involving JacobiNC:

Parity transformations and periodicity relations are automatically applied:

Automatic argument simplifications:

Representation in terms of trigonometric functions and JacobiAmplitude:

Relation to other Jacobi elliptic functions:

TraditionalForm formatting: