README.md (2506B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2018 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # fresnelc 22 23 > Compute the [Fresnel integral][fresnel-integral] C(x). 24 25 <section class="intro"> 26 27 The [Fresnel integral][fresnel-integral] C(x) is defined as 28 29 <!-- <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)"> --> 30 31 <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"> 32 <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)"> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 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)`. 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var fresnelc = require( '@stdlib/math/base/special/fresnelc' ); 50 ``` 51 52 #### fresnelc( x ) 53 54 Computes the [Fresnel integral][fresnel-integral] C(x). 55 56 ```javascript 57 var v = fresnelc( 0.0 ); 58 // returns ~0.0 59 60 v = fresnelc( 1.0 ); 61 // returns ~0.780 62 63 v = fresnelc( Infinity ); 64 // returns ~0.5 65 66 v = fresnelc( -Infinity ); 67 // returns ~-0.5 68 69 v = fresnelc( NaN ); 70 // returns NaN 71 ``` 72 73 </section> 74 75 <!-- /.usage --> 76 77 <section class="examples"> 78 79 ## Examples 80 81 <!-- eslint no-undef: "error" --> 82 83 ```javascript 84 var linspace = require( '@stdlib/array/linspace' ); 85 var fresnelc = require( '@stdlib/math/base/special/fresnelc' ); 86 87 var x = linspace( 0.0, 10.0, 100 ); 88 var i; 89 90 for ( i = 0; i < x.length; i++ ) { 91 console.log( fresnelc( x[ i ] ) ); 92 } 93 ``` 94 95 </section> 96 97 <!-- /.examples --> 98 99 <section class="links"> 100 101 [fresnel-integral]: https://en.wikipedia.org/wiki/Fresnel_integral 102 103 </section> 104 105 <!-- /.links -->