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

Installation

npm install @stdlib/math-base-special-beta

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 );
        }
    }
}

See Also

• @stdlib/math-base/special/betainc: incomplete beta function.
• @stdlib/math-base/special/betaincinv: inverse incomplete beta function.
• @stdlib/math-base/special/betaln: natural logarithm of the beta function.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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Copyright

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