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# `ellipticCE`

Complementary complete elliptic integral of the second kind

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## Syntax

```ellipticCE(`m`)
```

## Description

`ellipticCE(m)` represents the complementary complete elliptic integral of the second kind ${E}^{\prime }\left(m\right)=E\left(1-m\right)$, where $E\left(m\right)$ is the complete elliptic integral of the second kind:

`$E\left(m\right)=E\left(\frac{\pi }{2}|m\right)=\underset{0}{\overset{\pi /2}{\int }}\sqrt{1-m{\mathrm{sin}}^{2}\theta }\text{\hspace{0.17em}}d\theta$`

The complementary complete elliptic integral of the second kind is defined for a complex argument m.

For floating-point values `m`, `ellipticCE(m)` returns floating-point results. For most exact arguments, it returns unevaluated symbolic calls. You can approximate such results with floating-point numbers using the `float` function.

## Environment Interactions

When called with floating-point arguments, this function is sensitive to the environment variable `DIGITS` which determines the numerical working precision.

## Examples

### Example 1

Most calls with exact arguments return themselves unevaluated. To approximate such values with floating-point numbers, use `float`:

```ellipticCE(PI/4); float(ellipticCE(PI/4))```
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Alternatively, use a floating-point value as an argument:

```ellipticCE(1/2); ellipticCE(0.5)```
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`ellipticCE(0)` and `ellipticCE(1)` have special values:

`ellipticCE(0)`
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`ellipticCE(1)`
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## Parameters

 `m` An arithmetical expression specifying the parameter.

## Return Values

Arithmetical expression.

#### Mathematical Modeling with Symbolic Math Toolbox

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