beta

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

beta( x, y )

Evaluates the beta function.

var val = beta( 0.0, 0.5 );
// returns Infinity

val = beta( 1.0, 1.0 );
// returns 1.0

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

val = beta( 5.0, 0.2 );
// returns ~3.382

val = beta( 4.0, 1.0 );
// returns 0.25

Examples

var beta = require( '@stdlib/math/base/special/beta' );
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, beta( x, y ) );
    }
}

C APIs

Usage

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

stdlib_base_beta( a, b )

Evaluates the beta function.

double out = stdlib_base_beta( 1.0, 1,0 );
// returns 1.0

out = stdlib_base_beta( 5.0, 0.2);
// returns ~3.382

The function accepts the following arguments:

a: [in] double input value.
b: [in] double input value.

double stdlib_base_beta ( const double a, const double b );

Examples

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

int main( void ) {
    const double x[] = { 1.0, 3.0, 5.0, 8.0, 10.0 };
    const double y[] = { 2.0, 4.0, 7.0, 9.0, 10.0 };

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