Documentation

# `ellipticNome`

Elliptic nome

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## Syntax

```ellipticNome(`m`)
```

## Description

`ellipticNome(m)` represents the elliptic nome q which is defined as

`$q\left(m\right)={e}^{-\frac{\pi {K}^{\prime }\left(m\right)}{K\left(m\right)}}$`

The elliptic nome $q\left(m\right)$ is defined for complex arguments m.

$|q\left(m\right)|\le 1$ holds for all $m\in ℂ$.

## 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 exact arguments, `ellipticNome` returns unevaluated:

```ellipticNome(1/3), ellipticNome(2), ellipticNome(I)```
` `

To approximate such values with floating-point numbers, use `float`:

`float(ellipticNome(3/4))`
` `

Alternatively, use a floating-point value as an argument:

`ellipticNome(0.5)`
` `

For `m = 0`, `m = 1/2`, and ```m = 1```, `ellipticNome` returns explicit results:

```ellipticNome(0), ellipticNome(1/2), ellipticNome(1)```
` `

## Parameters

 `m` An arithmetical expression specifying the parameter.

## Return Values

Arithmetical expression.