fresnel

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

The Fresnel integrals are defined as

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).

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/math/utils/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 ] ) );
}