# InverseJacobiND

InverseJacobiND[v,m]

gives the inverse Jacobi elliptic function .

# Details

• Mathematical function, suitable for both symbolic and numerical manipulation.
• gives the value of for which .
• InverseJacobiND 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.
• The inverse Jacobi elliptic functions are related to elliptic integrals.
• For certain special arguments, InverseJacobiND automatically evaluates to exact values.
• InverseJacobiND can be evaluated to arbitrary numerical precision.
• InverseJacobiND automatically threads over lists.

# Examples

open allclose all

## Basic Examples(5)

Evaluate numerically:

Plot the function over a subset of the reals:

Plot the imaginary part of the function:

Plot over a subset of the complexes:

Series expansions at the origin:

Series expansion at Infinity:

## Scope(26)

### Numerical Evaluation(3)

Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate InverseJacobiND efficiently at high precision:

### Specific Values(3)

Simple exact results are generated automatically:

Values at infinity:

Find a real root of the equation :

### Visualization(3)

Plot InverseJacobiND for various values of the second parameter :

Plot InverseJacobiND as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

### Function Properties(6)

InverseJacobiND 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 InverseJacobiND with respect to the second argument :

Plot higher derivatives for :

### Series Expansions(3)

Taylor expansion for around :

Plot the first three approximations for around :

Series expansion for around :

InverseJacobiND can be applied to a power series:

### Function Identities and Simplifications(2)

InverseJacobiND is the inverse function of JacobiND:

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 InverseJacobiND from solving equations containing elliptic functions:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_inversejacobind, author="Wolfram Research", title="{InverseJacobiND}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/InverseJacobiND.html}", note=[Accessed: 23-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversejacobind, organization={Wolfram Research}, title={InverseJacobiND}, year={1988}, url={https://reference.wolfram.com/language/ref/InverseJacobiND.html}, note=[Accessed: 23-April-2024 ]}