betaln

Natural logarithm of the Beta function.

The Beta function, also called the Euler integral, is defined as

upper B e t a left-parenthesis x comma y right-parenthesis equals integral Subscript 0 Superscript 1 Baseline t Superscript x minus 1 Baseline left-parenthesis 1 minus t right-parenthesis Superscript y minus 1 Baseline normal d t

The Beta function is related to the Gamma function via the following equation

upper B e t a left-parenthesis x comma y right-parenthesis equals StartFraction normal upper Gamma left-parenthesis x right-parenthesis normal upper Gamma left-parenthesis y right-parenthesis Over normal upper Gamma left-parenthesis x plus y right-parenthesis EndFraction

Usage

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

betaln( x, y )

Evaluates the the natural logarithm of the beta function.

var val = betaln( 0.0, 0.0 );
// returns Infinity

val = betaln( 1.0, 1.0 );
// returns 0.0

val = betaln( -1.0, 2.0 );
// returns NaN

val = betaln( 5.0, 0.2 );
// returns ~1.218

val = betaln( 4.0, 1.0 );
// returns ~-1.386

Examples

var betaln = require( '@stdlib/math/base/special/betaln' );
var x;
var y;

for ( x = 0; x < 10; x++ ) {
    for ( y = 10; y > 0; y-- ) {
        console.log( 'x: %d, \t y: %d, \t f(x,y): %d', x, y, betaln( x, y ) );
    }
}