@stdlib/math-base-special-gamma

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Gamma Function

Gamma function.

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

-->

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

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 ] ) );
}

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See Also

• @stdlib/math-base/special/gamma1pm1: compute gamma(x+1) - 1.
• @stdlib/math-base/special/gammainc: incomplete gamma function.
• @stdlib/math-base/special/gammaincinv: inverse incomplete gamma function.
• @stdlib/math-base/special/gammaln: natural logarithm of the gamma 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

Copyright © 2016-2023. The Stdlib Authors.

Changelog

0.1.0 (2023-09-24)

<section class="features">

Features

• 58832ee - update minimum TypeScript version

</section> <!-- /.features --> <section class="breaking-changes">

BREAKING CHANGES

• 58832ee: update minimum TypeScript version to 4.1

  • To migrate, users should upgrade their TypeScript version to at least version 4.1.

</section> <!-- /.breaking-changes --> <section class="commits">

Commits

<details>

• 58832ee - feat: update minimum TypeScript version (by Philipp Burckhardt)
• a37ebe2 - docs: remove empty lines (by Philipp Burckhardt)
• b734544 - refactor: use strictEqual checks (by Philipp Burckhardt)
• c5da1f9 - docs: render equations via math code blocks (by Philipp Burckhardt)

</details> </section> <!-- /.commits --> <section class="contributors">

Contributors

A total of 1 person contributed to this release. Thank you to this contributor:

• Philipp Burckhardt

</section> <!-- /.contributors --> </section> <!-- /.release --> <section class="release" id="v0.0.6">