# InverseJacobiNC

InverseJacobiNC[v,m]

gives the inverse Jacobi elliptic function .

# Details

• Mathematical function, suitable for both symbolic and numerical manipulation.
• gives the value of for which .
• InverseJacobiNC has branch cut discontinuities in the complex plane with branch points at and infinity, and in the complex m plane with branch points at and infinity.
• The inverse Jacobi elliptic functions are related to elliptic integrals.
• For certain special arguments, InverseJacobiNC automatically evaluates to exact values.
• InverseJacobiNC can be evaluated to arbitrary numerical precision.
• InverseJacobiNC automatically threads over lists.

# Examples

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## Basic Examples(5)

Evaluate numerically:

Check defining property:

Plot the function over a subset of the reals:

Plot over a subset of the complexes:

Series expansion at the origin:

Series expansion at Infinity:

## Scope(26)

### Numerical Evaluation(3)

Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate InverseJacobiNC efficiently at high precision:

### Specific Values(3)

Simple exact values are generated automatically:

Value at infinity:

Find a real root of the equation :

### Visualization(3)

Plot InverseJacobiNC for various values of the second parameter :

Plot InverseJacobiNC as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

### Function Properties(6)

InverseJacobiNC is not an analytic function:

It has both singularities and discontinuities:

is nondecreasing on its real domain:

is injective:

is not surjective:

is non-negative on its real domain:

is concave on its real domain:

### Differentiation(4)

First derivative:

Higher derivatives:

Plot higher derivatives for :

Differentiate InverseJacobiNC with respect to the second argument :

Plot higher derivatives for :

### Series Expansions(3)

Taylor expansion for around :

Plot the first three approximations for around :

Taylor expansion for around :

Plot the first three approximations for around :

InverseJacobiNC can be applied to a power series:

### Function Identities and Simplifications(2)

InverseJacobiNC is the inverse function of JacobiNC:

Compose with inverse function:

Use PowerExpand to disregard multivaluedness of the inverse function:

## Applications(1)

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

## Properties & Relations(1)

Obtain InverseJacobiNC from solving equations containing elliptic functions:

Wolfram Research (1988), InverseJacobiNC, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiNC.html.

#### Text

Wolfram Research (1988), InverseJacobiNC, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseJacobiNC.html.

#### CMS

Wolfram Language. 1988. "InverseJacobiNC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseJacobiNC.html.

#### APA

Wolfram Language. (1988). InverseJacobiNC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseJacobiNC.html

#### BibTeX

@misc{reference.wolfram_2024_inversejacobinc, author="Wolfram Research", title="{InverseJacobiNC}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/InverseJacobiNC.html}", note=[Accessed: 19-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversejacobinc, organization={Wolfram Research}, title={InverseJacobiNC}, year={1988}, url={https://reference.wolfram.com/language/ref/InverseJacobiNC.html}, note=[Accessed: 19-June-2024 ]}