ellipticCK

Complementary complete elliptic integral of the first kind

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

```ellipticCK(`m`)
```

Description

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

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

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

For floating-point values `m`, `ellipticCK(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`:

```ellipticCK(PI/4); float(ellipticCK(PI/4))```
``` ```
``` ```

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

```ellipticCK(1/2); ellipticCK(0.5)```
``` ```
``` ```

`ellipticCK(1)` has a special value:

`ellipticCK(1)`
``` ```

Parameters

 `m` An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.