fresnelc

Compute the Fresnel integral C(x).

The Fresnel integral C(x) is defined as

$$C(x) = \int_0^x \cos\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t.$$

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

Usage

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

fresnelc( x )

Computes the Fresnel integral C(x).

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

v = fresnelc( 1.0 );
// returns ~0.780

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

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

v = fresnelc( NaN );
// returns NaN

Examples

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

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

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

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C APIs

Usage

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

stdlib_base_fresnelc( x )

Computes the Fresnel integral C(x).

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

out = stdlib_base_fresnelc( 1.0 );
// returns ~0.780

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_fresnelc( const double x );

Examples

#include "stdlib/math/base/special/fresnelc.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_fresnelc( x[ i ] );
        printf( "fresnelc(%lf) = %lf\n", x[ i ], y );
    }
}

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See Also

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