Built-in Mathematica Symbol

InverseJacobiCS

InverseJacobiCS[v, m]
gives the inverse Jacobi elliptic function

.

InverseJacobiCS has branch cut discontinuities in the complex v plane with branch points at , and infinity, and in the complex m plane with branch points at and infinity.

For certain special arguments, InverseJacobiCS automatically evaluates to exact values.

Evaluate numerically:

Series expansion:

Evaluate for complex arguments:

Evaluate to high precision:

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

InverseJacobiCS threads element-wise over lists:

Simple exact results are generated automatically:

Parity transformation is automatically applied:

InverseJacobiCS can be applied to a power series:

Plot contours of constant real and imaginary parts in the complex plane:

Compose with inverse function:

Use PowerExpand to disregard multivaluedness of the inverse function:

Differentiate InverseJacobiCS:

Obtain InverseJacobiCS from solving equations containing elliptic functions:

Machine-precision input is insufficient to get a correct answer:

With exact input, the answer is correct: