Documentation

`ellipticNome`

Elliptic nome

MuPAD® notebooks will be removed in a future release. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

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.