erfc

Complementary error function.

The complementary error function is defined as

e r f c left-parenthesis x right-parenthesis equals 1 minus e r f left-parenthesis x right-parenthesis equals StartFraction 2 Over StartRoot pi EndRoot EndFraction integral Subscript x Superscript normal infinity Baseline e Superscript minus t squared Baseline d t

The complementary error function can also be expressed using Craig's formula

e r f c left-parenthesis x right-parenthesis equals StartFraction 2 Over pi EndFraction integral Subscript 0 Superscript StartFraction pi Over 2 EndFraction Baseline exp left-parenthesis minus StartFraction x squared Over sine squared theta EndFraction right-parenthesis d theta

Usage

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

erfc( x )

Evaluates the complementary error function.

var y = erfc( 2.0 );
// returns ~0.0047

y = erfc( -1.0 );
// returns ~1.8427

y = erfc( Infinity );
// returns 0.0

y = erfc( -Infinity );
// returns 2.0

If provided NaN, the function returns NaN.

var y = erfc( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/math/utils/linspace' );
var erfc = require( '@stdlib/math/base/special/erfc' );

var x = linspace( -10.0, 10.0, 100 );
var y;
var i;

for ( i = 0; i < x.length; i++ ) {
    y = erfc( x[ i ] );
    console.log( 'x: %d, erfc(x): %d', x[ i ], y );
}