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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

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When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

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erfc

NPM version Build Status Coverage Status

Complementary error function.

The complementary error function is defined as

erfc ( x ) = 1 erf ( x ) = 2 π x e t 2 d t

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

erfc ( x ) = 2 π 0 π 2 exp ( x 2 sin 2 θ ) d θ

Installation

npm install @stdlib/math-base-special-erfc

Alternatively,

  • To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
  • If you are using Deno, visit the deno branch (see README for usage intructions).
  • For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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

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

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

C APIs

Usage

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

stdlib_base_erfc( x )

Evaluates the complementary error function.

double out = stdlib_base_erfc( 2.0 );
// returns ~0.0047

out = stdlib_base_erfc( -1.0 );
// returns ~1.8427

The function accepts the following arguments:

  • x: [in] double input value.
double stdlib_base_erfc( const double x );

Examples

#include "stdlib/math/base/special/erfc.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    const double x[] = { -10.0, -7.78, -5.56, -3.33, -1.11, 1.11, 3.33, 5.56, 7.78, 10.0 };

    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_erfc( x[ i ] );
        printf( "x: %lf, erfc(x): %lf\n", x[ i ], v );
    }
}

See Also


Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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Copyright

Copyright © 2016-2025. The Stdlib Authors.