betaln

Natural logarithm of the beta function.

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

The beta function is related to the gamma function via the following equation

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 ) );
    }
}

C APIs

Usage

#include "stdlib/math/base/special/betaln.h"

stdlib_base_betaln( x, y )

Evaluates the the natural logarithm of the beta function.

double v = stdlib_base_betaln( 5.0, 0.2 );
// returns ~1.218

The function accepts the following arguments:

x: [in] double input value.
y: [in] double input value.

double stdlib_base_betaln( const double x, const double y );

Examples

#include "stdlib/math/base/special/betaln.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 24.0, 32.0, 48.0, 116.0, 33.0 };
    const double y[] = { 12.0, 6.0, 15.0, 52.0, 22.0 };

    double out;
    int i;
    for ( i = 0; i < 5; i++ ) {
        out = stdlib_base_betaln( x[ i ], y[ i ] );
        printf( "betaln(%lf, %lf) = %lf\n", x[ i ], y[ i ], out );
    }
}