fresnels

Compute the Fresnel integral S(x).

The Fresnel integral S(x) is defined as

Some sources define S(x) using t2 for the argument of the sine. To get this function, multiply the computed integral by √(π/2) and multiply the argument x by √(2/π).

Installation

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

Usage

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

fresnels( x )

Computes the Fresnel integral S(x).

var v = fresnels( 0.0 );
// returns ~0.0

v = fresnels( 1.0 );
// returns ~0.438

v = fresnels( Infinity );
// returns ~0.5

v = fresnels( -Infinity );
// returns ~-0.5

v = fresnels( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/array-base-linspace' );
var fresnels = require( '@stdlib/math-base-special-fresnels' );

var x = linspace( 0.0, 10.0, 100 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( fresnels( x[ i ] ) );
}

C APIs

Usage

#include "stdlib/math/base/special/fresnels.h"

stdlib_base_fresnels( x )

Computes the Fresnel integral S(x).

double out = stdlib_base_fresnels( 0.0 );
// returns ~0.0

out = stdlib_base_fresnels( 1.0 );
// returns ~0.438

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_fresnels( const double x );

Examples

#include "stdlib/math/base/special/fresnels.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.0, 3.14, 5.55, 10.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_fresnels( x[ i ] );
        printf( "fresnels(%lf) = %lf\n", x[ i ], y );
    }
}

See Also

• @stdlib/math-base/special/fresnel: compute the Fresnel integrals S(x) and C(x).
• @stdlib/math-base/special/fresnelc: compute the Fresnel integral C(x).

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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Copyright

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