betaln

Natural logarithm of the beta function.

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

$$\mathop{\mathrm{Beta}}(x,y) = \int_0^1t^{x-1}(1-t)^{y-1}\,\mathrm{d}t$$

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

$$\mathop{\mathrm{Beta}}(x,y)=\dfrac{\Gamma(x)\,\Gamma(y)}{\Gamma(x+y)} \!$$

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 ) );
    }
}

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See Also

• @stdlib/math/base/special/beta: beta function.
• @stdlib/math/base/special/betainc: incomplete beta function.
• @stdlib/math/base/special/betaincinv: inverse incomplete beta function.