@stdlib/math-base-special-gamma

Gamma function.

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README

Gamma Function

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Gamma function.

The gamma function extends the factorial function to real and complex numbers. If n is a positive integer,

Gamma function for positive integers.

Generalized to all complex numbers z, except for nonpositive integers, the gamma function can be expressed as an infinite product

Gamma function for all complex numbers.

where γ ≈ 0.577216 is the Euler–Mascheroni constant.

Installation

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

Usage

var gamma = require( '@stdlib/math-base-special-gamma' );

gamma( x )

Evaluates the gamma function.

var v = gamma( 4.0 );
// returns 6.0

v = gamma( -1.5 );
// returns ~2.363

v = gamma( -0.5 );
// returns ~-3.545

v = gamma( 0.5 );
// returns ~1.772

v = gamma( 0.0 );
// returns Infinity

v = gamma( -0.0 );
// returns -Infinity

v = gamma( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/array-base-linspace' );
var gamma = require( '@stdlib/math-base-special-gamma' );

var x = linspace( -10.0, 10.0, 100 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( 'x: %d, f(x): %d', x[ i ], gamma( x[ i ] ) );
}

See Also

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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License

See LICENSE.

Copyright

Copyright © 2016-2022. The Stdlib Authors.