Logarithm of Binomial Coefficient

Compute the natural logarithm of the binomial coefficient.

The natural logarithm of the binomial coefficient is

f left-parenthesis n comma k right-parenthesis equals ln StartBinomialOrMatrix n Choose k EndBinomialOrMatrix

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

StartBinomialOrMatrix n Choose k EndBinomialOrMatrix equals StartFraction n factorial Over k factorial left-parenthesis n minus k right-parenthesis factorial EndFraction for 0 less-than-or-equal-to k less-than-or-equal-to n

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

StartBinomialOrMatrix negative n Choose k EndBinomialOrMatrix equals left-parenthesis negative 1 right-parenthesis Superscript k Baseline StartBinomialOrMatrix n plus k minus 1 Choose k EndBinomialOrMatrix equals left-parenthesis negative 1 right-parenthesis Superscript k Baseline left-parenthesis StartBinomialOrMatrix n Choose k EndBinomialOrMatrix right-parenthesis

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 ~2.302

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 ) );
}