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# sici

> Compute the sine and cosine integrals.

<section class="intro">

The sine integral is defined as

<!-- <equation class="equation" label="eq:sine_integral" align="center" raw="\int_0^x \frac{\sin t}{t}\; dt" alt="Sine integral."> -->

<div class="equation" align="center" data-raw-text="\int_0^x \frac{\sin t}{t}\; dt" data-equation="eq:sine_integral">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/special/sici/docs/img/equation_sine_integral.svg" alt="Sine integral.">
    <br>
</div>

<!-- </equation> -->

and the cosine integral is defined as

<!-- <equation class="equation" label="eq:cosine_integral" align="center" raw="\gamma + \log( x ) + \int_0^x \frac{\cos t - 1}{t}\; dt" alt="Cosine integral."> -->

<div class="equation" align="center" data-raw-text="\gamma + \log( x ) + \int_0^x \frac{\cos t - 1}{t}\; dt" data-equation="eq:cosine_integral">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/special/sici/docs/img/equation_cosine_integral.svg" alt="Cosine integral.">
    <br>
</div>

<!-- </equation> -->

where `γ` is the [Euler-Mascheroni][eulergamma] constant.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### sici( \[out,] x )

Computes the sine and cosine integrals.

```javascript
var v = sici( 3.0 );
// returns [ ~1.849, ~0.12 ]

v = sici( 0.0 );
// returns [ 0.0, -Infinity ]

v = sici( -9.0 );
// returns [ ~-1.665, ~0.055 ]

v = sici( NaN );
// returns [ NaN, NaN ]
```

By default, the function returns the sine and cosine integrals as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 2 );

var v = sici( out, 3.0 );
// returns <Float64Array>[ ~1.849, ~0.12 ]

var bool = ( v === out );
// returns true
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var sici = require( '@stdlib/math/base/special/sici' );

var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 100.0;
    y = sici( x );
    console.log( 'si(%d) = %d, ci(%d) = %d', x, y[ 0 ], x, y[ 1 ] );
}
```

</section>

<!-- /.examples -->

<section class="links">

[eulergamma]: http://mathworld.wolfram.com/Euler-MascheroniConstant.html

</section>

<!-- /.links -->
