Evaluate numerically to high precision:

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

Evaluate for complex arguments:

Evaluate JacobiNC efficiently at high precision:

Compute average case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix JacobiNC function using MatrixFunction:

Simple exact values are generated automatically:

Some poles of JacobiNC:

Find a local maximum of JacobiNC as a root of :

Plot the JacobiNC functions for various parameter values:

Plot JacobiNC as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

JacobiNC is -periodic along the real axis:

JacobiNC is -periodic along the imaginary axis:

JacobiNC is an even function in its first argument:

is an analytic function of for :

It has both singularities and discontinuities for :

is neither nondecreasing nor nonincreasing:

is not injective for any fixed :

is not surjective for any fixed :

JacobiNC is non-negative nor for :

In general, it has indeterminate sign:

JacobiNC is neither convex nor concave:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Derivative with respect to :

Indefinite integral of JacobiNC:

Definite integral of JacobiNC:

More integrals:

Taylor expansion for :

Plot the first three approximations for around :

Taylor expansion for :

Plot the first three approximations for around :

JacobiNC can be applied to power series:

Parity transformations and periodicity relations are automatically applied:

Identity involving JacobiSC:

Argument simplifications:

Representation in terms of Sec of JacobiAmplitude:

Relation to other Jacobi elliptic functions:

TraditionalForm formatting: