npm package: @stdlib/math-base-special-binomcoefln
Description: Compute the natural logarithm of the binomial coefficient.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Logarithm of Binomial Coefficient

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the natural logarithm of the [binomial coefficient][binomial-coefficient].

<section class="intro">

The natural logarithm of the [binomial coefficient][binomial-coefficient] is

<!-- <equation class="equation" label="eq:binomcoefln_function" align="center" raw="f(n,k) = \ln {n \choose k}" alt="Natural logarithm of the binomial coefficient."> -->

<div class="equation" align="center" data-raw-text="f(n,k) = \ln {n \choose k}" data-equation="eq:binomcoefln_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/binomcoefln/docs/img/equation_binomcoefln_function.svg" alt="Natural logarithm of the binomial coefficient.">
    <br>
</div> -->

<!-- </equation> -->

The [binomial coefficient][binomial-coefficient] of two nonnegative integers `n` and `k` is defined as

<!-- <equation class="equation" label="eq:binomial_coefficient" align="center" raw="\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n" alt="Factorial formula for the Binomial coefficient."> -->

<!-- <div class="equation" align="center" data-raw-text="\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n" data-equation="eq:binomial_coefficient">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/binomcoefln/docs/img/equation_binomial_coefficient.svg" alt="Factorial formula for the Binomial coefficient.">
    <br>
</div> -->

<!-- </equation> -->

The [binomial coefficient][binomial-coefficient] can be generalized to negative integers `n` as follows:

<!-- <equation class="equation" label="eq:binomial_coefficient_negative_integers" align="center" raw="\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)" alt="Generalization of the binomial coefficient to negative n."> -->

<!-- <div class="equation" align="center" data-raw-text="\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)" data-equation="eq:binomial_coefficient_negative_integers">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/math/base/special/binomcoefln/docs/img/equation_binomial_coefficient_negative_integers.svg" alt="Generalization of the binomial coefficient to negative n.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-binomcoefln
```

</section>

<section class="usage">

## Usage

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

#### binomcoefln( n, k )

Evaluates the natural logarithm of the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.

```javascript
var v = binomcoefln( 8, 2 );
// returns ~3.332

v = binomcoefln( 0, 0 );
// returns 0.0

v = binomcoefln( -4, 2 );
// returns ~2.303

v = binomcoefln( 88, 3 );
// returns ~11.606

v = binomcoefln( NaN, 3 );
// returns NaN

v = binomcoefln( 5, NaN );
// returns NaN

v = binomcoefln( NaN, NaN );
// returns NaN
```

For negative `k`, the function returns `-Infinity`.

```javascript
var v = binomcoefln( 2, -1 );
// returns -Infinity

v = binomcoefln( -3, -1 );
// returns -Infinity
```

The function returns `NaN` for non-integer `n` or `k`.

```javascript
var v = binomcoefln( 2, 1.5 );
// returns NaN

v = binomcoefln( 5.5, 2 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var binomcoefln = require( '@stdlib/math-base-special-binomcoefln' );

var opts = {
    'dtype': 'float64'
};
var n = discreteUniform( 100, -10, 30, opts );
var k = discreteUniform( 100, 0, 20, opts );

logEachMap( 'ln( %d choose %d ) = %0.4f', n, k, binomcoefln );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/binomcoefln.h"
```

#### stdlib_base_binomcoefln( n, k )

Evaluates the natural logarithm of the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.

```c
double v = stdlib_base_binomcoefln( 8.0, 2.0 );
// returns ~3.332
```

The function accepts the following arguments:

-   **n**: `[in] double` input value.
-   **k**: `[in] double` input value.

```c
double stdlib_base_binomcoefln( const double n, const double k );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/binomcoefln.h"
#include <stdio.h>

int main( void ) {
    const double a[] = { 24.0, 32.0, 48.0, 116.0, 33.0 };
    const double b[] = { 12.0, 6.0, 15.0, 52.0, 22.0 };

    double out;
    int i;
    for ( i = 0; i < 5; i++ ) {
        out = stdlib_base_binomcoefln( a[ i ], b[ i ] );
        printf( "binomcoefln(%lf, %lf) = %lf\n", a[ i ], b[ i ], out );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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

<section class="related">

</section>

<!-- /.related -->

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* * *

## Notice

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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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