time-to-botec/squiggle/node_modules/@stdlib/math/base/special/binomcoefln
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Necessary in order to clearly see the squiggle hotwiring.
2022-12-03 12:44:49 +00:00
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Logarithm of Binomial Coefficient

Compute the natural logarithm of the binomial coefficient.

The natural logarithm of the binomial coefficient is

Natural logarithm of the binomial coefficient.

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

Factorial formula for the Binomial coefficient.

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

Generalization of the binomial coefficient to negative n.

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 ) );
}