# ellipticNome

Elliptic nome function

## Syntax

``ellipticNome(m)``

## Description

example

````ellipticNome(m)` returns the Elliptic Nome of `m`. If `m` is an array, then `ellipticNome` acts element-wise.```

## Examples

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`ellipticNome(1.3)`
```ans = 0.0881 - 0.2012i```

Call `ellipticNome` on array inputs. `ellipticNome` acts element-wise when `m` is an array.

`ellipticNome([2 1 -3/2])`
```ans = 0.0000 - 0.2079i 1.0000 + 0.0000i -0.0570 + 0.0000i```

Convert numeric input to symbolic form using `sym`, and find the elliptic nome. For symbolic input where `m = 0`, `1/2`, or `1`, `ellipticNome` returns exact symbolic output.

`ellipticNome([0 1/2 1])`
```ans = 0 0.0432 1.0000```

Show that for any other symbolic values of `m`, `ellipticNome` returns an unevaluated function call.

`ellipticNome(sym(2))`
```ans = ellipticNome(2)```

For symbolic variables or expressions, `ellipticNome` returns the unevaluated function call.

```syms x f = ellipticNome(x)```
```f = ellipticNome(x)```

Substitute values for the variables by using `subs`, and convert values to double by using `double`.

`f = subs(f, x, 5)`
```f = ellipticNome(5)```
`fVal = double(f)`
```fVal = -0.1008 - 0.1992i```

Calculate `f` to higher precision using `vpa`.

`fVal = vpa(f)`
```fVal = - 0.10080189716733475056506021415746 - 0.19922973618609837873340100821425i```

Plot the real and imaginary values of the elliptic nome using `fcontour`. Fill plot contours by setting `Fill` to `on`.

```syms m f = ellipticNome(m); subplot(2,2,1) fcontour(real(f),'Fill','on') title('Real Values of Elliptic Nome') xlabel('m') subplot(2,2,2) fcontour(imag(f),'Fill','on') title('Imaginary Values of Elliptic Nome') xlabel('m')```

## Input Arguments

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Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

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### Elliptic Nome

The elliptic nome is

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

where K is the complete elliptic integral of the first kind, implemented as `ellipticK`.

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

Introduced in R2017b

## Support

#### Mathematical Modeling with Symbolic Math Toolbox

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