Logarithm of Binomial Coefficient

Compute the natural logarithm of the binomial coefficient.

The natural logarithm of the binomial coefficient is

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

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

Installation

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

Usage

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

binomcoefln( n, k )

Evaluates 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 ) );
}

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.