@stdlib/math-base-special-fresnel
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    fresnel

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    Compute the Fresnel integrals S(x) and C(x).

    The Fresnel integrals are defined as

    Fresnel integral

    Some sources define the Fresnel integrals using t2 for the argument of the sine and cosine. To get these functions, multiply the computed integrals by √(π/2) and multiply the argument x by √(2/π).

    Installation

    npm install @stdlib/math-base-special-fresnel

    Usage

    var fresnel = require( '@stdlib/math-base-special-fresnel' );

    fresnel( [out,] x )

    Simultaneously computes the Fresnel integrals S(x) and C(x).

    var v = fresnel( 0.0 );
    // returns [ ~0.0, ~0.0 ]
    
    v = fresnel( 1.0 );
    // returns [ ~0.438, ~0.780 ]
    
    v = fresnel( Infinity );
    // returns [ ~0.5, ~0.5 ]
    
    v = fresnel( -Infinity );
    // returns [ ~-0.5, ~-0.5 ]
    
    v = fresnel( NaN );
    // returns [ NaN, NaN ]

    By default, the function returns the S(x) and C(x) as a two-element array. To avoid extra memory allocation, the function supports providing an output (destination) object.

    var Float64Array = require( '@stdlib/array-float64' );
    
    var out = new Float64Array( 2 );
    
    var v = fresnel( out, 0.0 );
    // returns <Float64Array>[ ~0.0, ~0.0 ]
    
    var bool = ( v === out );
    // returns true

    Examples

    var linspace = require( '@stdlib/array-linspace' );
    var fresnel = require( '@stdlib/math-base-special-fresnel' );
    
    var x = linspace( 0.0, 10.0, 100 );
    var i;
    
    for ( i = 0; i < x.length; i++ ) {
        console.log( fresnel( x[ i ] ) );
    }

    Notice

    This package is part of 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, see the main project repository.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

    Install

    npm i @stdlib/math-base-special-fresnel

    Homepage

    stdlib.io

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    Version

    0.0.5

    License

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