BUILT-IN MATHEMATICA SYMBOL

InverseJacobiSN

gives the inverse Jacobi elliptic function

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InverseJacobiSN 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, InverseJacobiSN automatically evaluates to exact values.

Evaluate numerically:

Series expansion:

Evaluate numerically:

Out[1]=

Out[2]=

Out[1]=

Series expansion:

Out[1]=

Out[2]=

Evaluate for complex arguments:

Evaluate to high precision:

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

InverseJacobiSN threads element-wise over lists:

Simple exact results are generated automatically:

Parity transformation is automatically applied:

InverseJacobiSN 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:

Obtain InverseJacobiSN from solving equations containing elliptic functions:

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

With exact input, the answer is correct: