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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

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

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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.

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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.

Community

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Copyright

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