Beta Function / natural logarithm of the Beta function

Evaluates the beta function and the natural logarithm of the beta function.

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

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

It is related to the Gamma function via the following equation

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

and

$$\ln \mathrm{Beta}(x,y)= \ln \Gamma(x) + \ln \Gamma(y) - \ln \Gamma(x+y)$$

This package supports both CommonJs and ES Modules.

Installation

$ npm install @toshiara/special-beta

Usage

// for CommonJs
const { beta, betaln } = require('@toshiara/special-beta');

// for ES Modules
import { beta, betaln } from '@toshiara/special-beta';

beta(x, y)

Evaluates the beta function.

beta(1.2, 2.4);
// returns 0.3068371659652535

beta(0.1, 0.3);
// returns 12.8305985363213

betaln(x, y)

Evaluates the beta function.

betaln(1, 2);
// returns -0.6931471805599453

betaln(1.2, 2.4);
// returns -1.181438076130887

License

MIT license.