# Documentation

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# `jacobiNS`

Jacobi elliptic function ns

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## Syntax

```jacobiNS(`u`,`m`)
```

## Description

`jacobiNS(u,m)` represents the Jacobi elliptic function ns.

Let . Then the Jacobi elliptic function ns is defined as follows:

The Jacobi functions are defined for complex values of u and m.

The Jacobi functions are meromorphic and doubly periodic with periods and with respect to u.

For m = 0 and m = 1, the Jacobi functions reduce to trigonometric or constant functions.

If one argument is a floating-point number, and the other one can be converted to a floating-point number, then a floating-point number is returned.

## Environment Interactions

When called with floating-point arguments, these functions are sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

For most arguments, the Jacobi functions return themselves unevaluated:

`jacobiNS(2,1/2)`

Floating-point numbers are returned if at least one of the arguments is a floating-point number:

`jacobiNS(1.5,1/2)`

Floating-point evaluation can be enforced by using `float`:

`float(jacobiNS(1,-1))`

### Example 2

For m = 0 and m = 1, the result is expressed using a trigonometric function:

`jacobiNS(u,0)`

`jacobiNS(u,1)`

## Parameters

 `m` An arithmetical expression specifying the parameter.

## Return Values

Arithmetical expression.