Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate InverseJacobiCN efficiently at high precision:

InverseJacobiCN threads elementwise over lists:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix InverseJacobiCN function using MatrixFunction:

Simple exact values are generated automatically:

Value at infinity:

Find a real root of the equation :

Plot InverseJacobiCN for various values of the second parameter :

Plot InverseJacobiCN as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

InverseJacobiCN is not an analytic function:

It has both singularities and discontinuities:

is nonincreasing on its real domain:

is injective:

is not surjective:

is non-negative on its real domain:

is neither convex nor concave on its real domain:

First derivative:

Higher derivatives:

Differentiate InverseJacobiCN with respect to the second argument :

Higher derivatives:

Taylor expansion for :

Plot the first three approximations for around :

Taylor expansion for :

Plot the first three approximations for around :

InverseJacobiCN is the inverse function of JacobiCN:

Compose with the inverse function:

Use PowerExpand to disregard multivaluedness of the inverse function:

InverseJacobiCN can be applied to a power series:

TraditionalForm formatting: