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# fresnelc

> Compute the [Fresnel integral][fresnel-integral] C(x).

<section class="intro">

The [Fresnel integral][fresnel-integral] C(x) is defined as

<!-- <equation class="equation" label="eq:fresnel_integral" align="center" raw="C(x) = \int_0^x \cos\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t." alt="Fresnel integral C(x)"> -->

<div class="equation" align="center" data-raw-text="C(x) = \int_0^x \cos\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t." data-equation="eq:fresnel_integral">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/math/base/special/fresnelc/docs/img/equation_fresnel_integral.svg" alt="Fresnel integral C(x)">
    <br>
</div>

<!-- </equation> -->

Some sources define C(x) using t<sup>2</sup> for the argument of the cosine. To get this function, multiply the computed integral by `√(π/2)` and multiply the argument `x` by `√(2/π)`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var fresnelc = require( '@stdlib/math/base/special/fresnelc' );
```

#### fresnelc( x )

Computes the [Fresnel integral][fresnel-integral] C(x).

```javascript
var v = fresnelc( 0.0 );
// returns ~0.0

v = fresnelc( 1.0 );
// returns ~0.780

v = fresnelc( Infinity );
// returns ~0.5

v = fresnelc( -Infinity );
// returns ~-0.5

v = fresnelc( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var linspace = require( '@stdlib/array/base/linspace' );
var fresnelc = require( '@stdlib/math/base/special/fresnelc' );

var x = linspace( 0.0, 10.0, 100 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( fresnelc( x[ i ] ) );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/fresnelc.h"
```

#### stdlib_base_fresnelc( x )

Computes the [Fresnel integral][fresnel-integral] C(x).

```c
double out = stdlib_base_fresnelc( 0.0 );
// returns ~0.0

out = stdlib_base_fresnelc( 1.0 );
// returns ~0.780
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_fresnelc( const double x );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/fresnelc.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.0, 3.14, 5.55, 10.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_fresnelc( x[ i ] );
        printf( "fresnelc(%lf) = %lf\n", x[ i ], y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/fresnel`][@stdlib/math/base/special/fresnel]</span><span class="delimiter">: </span><span class="description">compute the Fresnel integrals S(x) and C(x).</span>
-   <span class="package-name">[`@stdlib/math/base/special/fresnels`][@stdlib/math/base/special/fresnels]</span><span class="delimiter">: </span><span class="description">compute the Fresnel integral S(x).</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[fresnel-integral]: https://en.wikipedia.org/wiki/Fresnel_integral

<!-- <related-links> -->

[@stdlib/math/base/special/fresnel]: https://github.com/stdlib-js/math/tree/main/base/special/fresnel

[@stdlib/math/base/special/fresnels]: https://github.com/stdlib-js/math/tree/main/base/special/fresnels

<!-- </related-links> -->

</section>

<!-- /.links -->
