131 lines
3.2 KiB
Markdown
131 lines
3.2 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# sici
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> Compute the sine and cosine integrals.
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<section class="intro">
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The sine integral is defined as
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<!-- <equation class="equation" label="eq:sine_integral" align="center" raw="\int_0^x \frac{\sin t}{t}\; dt" alt="Sine integral."> -->
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<div class="equation" align="center" data-raw-text="\int_0^x \frac{\sin t}{t}\; dt" data-equation="eq:sine_integral">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/sici/docs/img/equation_sine_integral.svg" alt="Sine integral.">
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<br>
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</div>
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<!-- </equation> -->
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and the cosine integral is defined as
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<!-- <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."> -->
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<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">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/sici/docs/img/equation_cosine_integral.svg" alt="Cosine integral.">
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<br>
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</div>
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<!-- </equation> -->
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where `γ` is the [Euler-Mascheroni][eulergamma] constant.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var sici = require( '@stdlib/math/base/special/sici' );
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```
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#### sici( \[out,] x )
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Computes the sine and cosine integrals.
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```javascript
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var v = sici( 3.0 );
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// returns [ ~1.849, ~0.12 ]
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v = sici( 0.0 );
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// returns [ 0.0, -Infinity ]
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v = sici( -9.0 );
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// returns [ ~-1.665, ~0.055 ]
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v = sici( NaN );
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// returns [ NaN, NaN ]
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```
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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.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var out = new Float64Array( 2 );
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var v = sici( out, 3.0 );
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// returns <Float64Array>[ ~1.849, ~0.12 ]
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var bool = ( v === out );
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// returns true
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var sici = require( '@stdlib/math/base/special/sici' );
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var x;
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var y;
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var i;
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for ( i = 0; i < 100; i++ ) {
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x = randu() * 100.0;
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y = sici( x );
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console.log( 'si(%d) = %d, ci(%d) = %d', x, y[ 0 ], x, y[ 1 ] );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[eulergamma]: http://mathworld.wolfram.com/Euler-MascheroniConstant.html
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</section>
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<!-- /.links -->
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