@stdlib/math-base-special-betaln
v0.3.1TypeScript
Natural logarithm of the beta function.
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Published by The Stdlib Authors
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betaln
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> [Natural logarithm][natural-logarithm] of the [beta function][beta-function].
The [beta function][beta-function], also called the Euler integral, is defined as
The [beta function][beta-function] is related to the [gamma function][gamma-function] via the following equation
Installation
``bash`
npm install @stdlib/math-base-special-betaln
Usage
`javascript`
var betaln = require( '@stdlib/math-base-special-betaln' );
#### betaln( x, y )
Evaluates the [natural logarithm][natural-logarithm] of the [beta function][beta-function].
`javascript
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
`javascript
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
$3
`c`
#include "stdlib/math/base/special/betaln.h"
#### stdlib_base_betaln( x, y )
Evaluates the [natural logarithm][natural-logarithm] of the [beta function][beta-function].
`c`
double v = stdlib_base_betaln( 5.0, 0.2 );
// returns ~1.218
The function accepts the following arguments:
- x: [in] double input value.[in] double
- y: input value.
`c`
double stdlib_base_betaln( const double x, const double y );
$3
`c
#include "stdlib/math/base/special/betaln.h"
#include
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 );
}
}
`
*
See Also
- [@stdlib/math-base/special/beta][@stdlib/math/base/special/beta]: beta function.
- [@stdlib/math-base/special/betainc][@stdlib/math/base/special/betainc]: incomplete beta function.
- [@stdlib/math-base/special/betaincinv][@stdlib/math/base/special/betaincinv]: inverse incomplete beta function.
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-betaln/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-betaln/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-betaln/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-betaln/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-betaln/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-betaln/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-betaln/blob/main/branches.md
[natural-logarithm]: https://en.wikipedia.org/wiki/Natural_logarithm
[beta-function]: https://en.wikipedia.org/wiki/Beta_function
[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
[@stdlib/math/base/special/beta]: https://www.npmjs.com/package/@stdlib/math-base-special-beta
[@stdlib/math/base/special/betainc]: https://www.npmjs.com/package/@stdlib/math-base-special-betainc
[@stdlib/math/base/special/betaincinv]: https://www.npmjs.com/package/@stdlib/math-base-special-betaincinv