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).

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 );
    }
}