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Logarithm of Binomial Coefficient
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Compute the natural logarithm of the [binomial coefficient][binomial-coefficient].
n and k is defined as
The [binomial coefficient][binomial-coefficient] can be generalized to negative integers n as follows:
bash
npm install @stdlib/math-base-special-binomcoefln
javascript
var binomcoefln = require( '@stdlib/math-base-special-binomcoefln' );
#### binomcoefln( n, k )
Evaluates 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
javascript
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 ) );
}
