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Logarithm of Binomial Coefficient

Compute the natural logarithm of the binomial coefficient.

The natural logarithm of the binomial coefficient is

$$f(n,k) = \ln {n \choose k}$$

The binomial coefficient of two nonnegative integers n and k is defined as

$$\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n$$

The binomial coefficient can be generalized to negative integers n as follows:

$$\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)$$

Installation

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

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

binomcoefln( n, k )

Evaluates the natural logarithm of the binomial coefficient of two integers n and k.

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.

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

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

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

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

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

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var binomcoefln = require( '@stdlib/math-base-special-binomcoefln' );

var n;
var k;
var i;

for ( i = 0; i < 100; i++ ) {
    n = round( (randu()*40.0) - 10.0 );
    k = round( randu()*20.0 );
    console.log( 'ln( %d choose %d ) = %d', n, k, binomcoefln( n, k ) );
}

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C APIs

Usage

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

stdlib_base_binomcoefln( n, k )

Evaluates the natural logarithm of the binomial coefficient of two integers n and k.

double v = stdlib_base_binomcoefln( 8, 2 );
// returns ~3.332

The function accepts the following arguments:

• n: [in] int64_t input value.
• k: [in] int64_t input value.

double stdlib_base_binomcoefln( const int64_t n, const int64_t k );

Examples

#include "stdlib/math/base/special/binomcoefln.h"
#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>

int main( void ) {
    const int64_t a[] = { 24, 32, 48, 116, 33 };
    const int64_t b[] = { 12, 6, 15, 52, 22 };

    double out;
    int i;
    for ( i = 0; i < 5; i++ ) {
        out = stdlib_base_binomcoef( a[ i ], b[ i ] );
        printf( "binomcoefln(%" PRId64 ", %" PRId64 ") = %lf\n", a[ i ], b[ i ], out );
    }
}

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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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.