time-to-botec/js/node_modules/@stdlib/math/base/special/erfc/README.md

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@license Apache-2.0
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# erfc
> [Complementary error function][complementary-error-function].
<section class="intro">
The [complementary error function][complementary-error-function] is defined as
<!-- <equation class="equation" label="eq:complementary_error_function" align="center" raw="\operatorname{erfc}(x) = 1 - \operatorname{erf}(x) = \frac{2}{\sqrt\pi} \int_x^{\infty} e^{-t^2}\, dt" alt="Complementary error function."> -->
<div class="equation" align="center" data-raw-text="\operatorname{erfc}(x) = 1 - \operatorname{erf}(x) = \frac{2}{\sqrt\pi} \int_x^{\infty} e^{-t^2}\, dt" data-equation="eq:complementary_error_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/erfc/docs/img/equation_complementary_error_function.svg" alt="Complementary error function.">
<br>
</div>
<!-- </equation> -->
The [complementary error function][complementary-error-function] can also be expressed using Craig's formula
<!-- <equation class="equation" label="eq:craigs_formula" align="center" raw="\operatorname{erfc}(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \exp \left( - \frac{x^2}{\sin^2 \theta} \right) d\theta" alt="Craig's formula of the complementary error function."> -->
<div class="equation" align="center" data-raw-text="\operatorname{erfc}(x) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \exp \left( - \frac{x^2}{\sin^2 \theta} \right) d\theta" data-equation="eq:craigs_formula">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/math/base/special/erfc/docs/img/equation_craigs_formula.svg" alt="Craig's formula of the complementary error function.">
<br>
</div>
<!-- </equation> -->
</section>
<!-- /.intro -->
<section class="usage">
## Usage
```javascript
var erfc = require( '@stdlib/math/base/special/erfc' );
```
#### erfc( x )
Evaluates the [complementary error function][complementary-error-function].
```javascript
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`.
```javascript
var y = erfc( NaN );
// returns NaN
```
</section>
<!-- /.usage -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var linspace = require( '@stdlib/array/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 );
}
```
</section>
<!-- /.examples -->
<section class="links">
[complementary-error-function]: https://en.wikipedia.org/wiki/Error_function
</section>
<!-- /.links -->