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# Kernel Betainc

> [Incomplete beta function][incomplete-beta-function] and its first derivative.

<section class="intro">

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var kernelBetainc = require( '@stdlib/math/base/special/kernel-betainc' );
```

#### kernelBetainc( x, a, b, regularized, upper )

Evaluates the [incomplete beta function][incomplete-beta-function] and its first derivative for parameters `x`, `a > 0` and `b > 0`. The `regularized` and `upper` boolean parameters are used to specify whether to evaluate the regularized or non-regularized and the upper or lower incomplete beta functions, respectively.

```javascript
var out = kernelBetainc( 0.8, 1.0, 0.3, false, false );
// returns [ ~1.277, ~0.926 ]

out = kernelBetainc( 0.2, 1.0, 2.0, true, false );
// returns [ 0.36, 1.6 ]

out = kernelBetainc( 0.2, 1.0, 2.0, true, true );
// returns [ 0.64, 1.6 ]
```

If provided `NaN` for `x`, `a`, or `b`, the function returns `[ NaN, NaN ]`.

```javascript
var out = kernelBetainc( NaN, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( 0.8, NaN, 1.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( 0.8, 1.0, NaN, true, true );
// returns [ NaN, NaN ]
```

If `x` is outside the interval `[0,1]`, the function returns `[ NaN, NaN ]`.

```javascript
var out = kernelBetainc( 1.5, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( -0.5, 1.0, 1.0, true, true );
// returns [ NaN, NaN ]
```

If `a` or `b` is negative, the function returns `[ NaN, NaN ]`.

```javascript
var out = kernelBetainc( 0.5, -2.0, 2.0, true, true );
// returns [ NaN, NaN ]

out = kernelBetainc( 0.5, 2.0, -2.0, true, true );
// returns [ NaN, NaN ]
```

#### kernelBetainc.assign( x, a, b, regularized, upper, out, stride, offset )

Evaluates the [incomplete beta function][incomplete-beta-function] and its first derivative for parameters `x`, `a > 0` and `b > 0` and assigns results to a provided output array.

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

var out = new Float64Array( 2 );
var v = kernelBetainc.assign( 0.2, 1.0, 2.0, true, true, out, 1, 0 );
// returns <Float64Array>[ 0.64, 1.6 ]

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

The `offset` parameter specifies the index of the first output array element, and the `stride` parameter specifies the stride length between consecutive output array elements.

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var kernelBetainc = require( '@stdlib/math/base/special/kernel-betainc' );

var out;
var i;
var x;
var a;
var b;

out = [ 0.0, 0.0 ];
for ( i = 0; i < 100; i++ ) {
    x = randu();
    a = randu() * 10.0;
    b = randu() * 10.0;
    kernelBetainc.assign( x, a, b, true, false, out, 1, 0 );
    console.log( 'x: %d, \t a: %d, \t b: %d, \t f(x,a,b): %d, \t f^1(x,a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), out[ 0 ].toFixed( 4 ), out[ 1 ].toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/betainc`][@stdlib/math/base/special/betainc]</span><span class="delimiter">: </span><span class="description">incomplete beta function.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function

<!-- <related-links> -->

[@stdlib/math/base/special/betainc]: https://github.com/stdlib-js/math/tree/main/base/special/betainc

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</section>

<!-- /.links -->
