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.

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.