Evaluate numerically to high precision:

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

Evaluate for complex arguments:

Evaluate JacobiSC efficiently at high precision:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix JacobiSC function using MatrixFunction:

Simple exact values are generated automatically:

Some poles of JacobiSC:

Find a local inflection point of JacobiSC as a root of :

Plot the JacobiSC functions for various parameter values:

Plot JacobiSC as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

JacobiSC is -periodic along the real axis:

JacobiSC is -periodic along the imaginary axis:

JacobiSC is an odd function in its first argument:

is an analytic function of for :

It is not, in general, analytic:

It has both singularities and discontinuities for :

is neither nondecreasing nor nonincreasing:

JacobiSC is not injective for any fixed

It is injective for :

is not surjective for :

It is surjective for :

JacobiSC is neither non-negative nor non-positive:

JacobiSC is neither convex nor concave:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Derivative with respect to :

Indefinite integral of JacobiSC:

Definite integral of JacobiSC:

More integrals:

Taylor expansion for :

Plot the first three approximations for around :

Taylor expansion for :

Plot the first three approximations for around :

JacobiSC can be applied to a power series:

Parity transformation and periodicity relations are automatically applied:

Identity involving JacobiNC:

Argument simplifications:

Representation in terms of Tan of JacobiAmplitude:

Relation to other Jacobi elliptic functions:

TraditionalForm formatting: