Built-in Mathematica Symbol

InverseJacobiDN

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

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

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

Evaluate numerically:

Series expansion:

Evaluate for complex arguments:

Evaluate to high precision:

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

InverseJacobiDN threads element-wise over lists:

Simple exact results are generated automatically:

InverseJacobiDN 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 InverseJacobiDN:

Obtain InverseJacobiDN from solving equations containing elliptic functions:

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

With exact input, the answer is correct: