npm package: @stdlib/math-base-special-sici
Description: Sine and cosine integrals.
Author: The Stdlib Authors
Latest version: 0.2.3

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# sici

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> 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.jsdelivr.net/gh/stdlib-js/stdlib@9d139bffba6eb2d0113c8412c1a9bf60ca59ac60/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.jsdelivr.net/gh/stdlib-js/stdlib@9d139bffba6eb2d0113c8412c1a9bf60ca59ac60/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="installation">

## Installation

```bash
npm install @stdlib/math-base-special-sici
```

</section>

<section class="usage">

## Usage

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

#### sici( 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 ]
```

#### sici.assign( x, out, stride, offset )

Computes the sine and cosine integrals and assigns results to a provided output array.

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

var out = new Float64Array( 2 );

var v = sici.assign( 3.0, out, 1, 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 for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

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---

## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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<section class="links">

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-sici.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-sici

[test-image]: https://github.com/stdlib-js/math-base-special-sici/actions/workflows/test.yml/badge.svg?branch=v0.2.3
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[stdlib]: https://github.com/stdlib-js/stdlib

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/math-base-special-sici/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-sici/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-sici/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-sici/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-sici/tree/esm
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[branches-url]: https://github.com/stdlib-js/math-base-special-sici/blob/main/branches.md

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

</section>

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