sici

Compute the sine and cosine integrals.

The sine integral is defined as

integral Subscript 0 Superscript x Baseline StartFraction sine t Over t EndFraction d t

and the cosine integral is defined as

gamma plus log left-parenthesis x right-parenthesis plus integral Subscript 0 Superscript x Baseline StartFraction cosine t minus 1 Over t EndFraction d t

where γ is the Euler-Mascheroni constant.

Usage

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

sici( [out,] x )

Computes the sine and cosine integrals.

var v = sici( 3.0 );
// returns [ ~1.849, ~0.12 ]

v = sici( 0.0 );
// returns [ 0.0, -Infinity ]

v = sici( -9.0 );
// returns [ ~-1.665, ~0.055 ]

v = sici( NaN );
// returns [ NaN, NaN ]

By default, the function returns the sine and cosine integrals as a two-element array. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 2 );

var v = sici( out, 3.0 );
// returns <Float64Array>[ ~1.849, ~0.12 ]

var bool = ( v === out );
// returns true

Examples

var randu = require( '@stdlib/random/base/randu' );
var sici = require( '@stdlib/math/base/special/sici' );

var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 100.0;
    y = sici( x );
    console.log( 'si(%d) = %d, ci(%d) = %d', x, y[ 0 ], x, y[ 1 ] );
}