fresnels

Compute the Fresnel integral S(x).

The Fresnel integral S(x) is defined as

upper S left-parenthesis x right-parenthesis equals integral Subscript 0 Superscript x Baseline sine left-parenthesis StartFraction pi Over 2 EndFraction t squared right-parenthesis normal d t period

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/math/utils/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 ] ) );
}