@stdlib/math-base-special-gamma
v0.3.1TypeScript
Gamma function.
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Published by The Stdlib Authors
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About stdlib...
Gamma Function
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> [Gamma][gamma-function] function.
The [gamma function][gamma-function] extends the [factorial function][@stdlib/math/base/special/factorial] to [real][real] and [complex][complex] numbers. If n is a positive integer,
Generalized to all complex numbers z, except for nonpositive integers, the [gamma function][gamma-function] can be expressed as an infinite product
where γ ≈ 0.577216 is the [Euler–Mascheroni constant][@stdlib/constants/float64/eulergamma].
Installation
``bash`
npm install @stdlib/math-base-special-gamma
Usage
`javascript`
var gamma = require( '@stdlib/math-base-special-gamma' );
#### gamma( x )
Evaluates the [gamma function][gamma-function].
`javascript
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
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var gamma = require( '@stdlib/math-base-special-gamma' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, -10.0, 10.0, opts );
logEachMap( 'x: %0.4f, f(x): %0.4f', x, gamma );
`
*
C APIs
$3
`c`
#include "stdlib/math/base/special/gamma.h"
#### stdlib_base_gamma( x )
Evaluates the [gamma function][gamma-function].
`c
double out = stdlib_base_gamma( 4.0 );
// returns 6.0
out = stdlib_base_gamma( -1.5 );
// returns ~2.363
`
The function accepts the following arguments:
- x: [in] double input value.
`c`
double stdlib_base_gamma( const double x );
$3
`c
#include "stdlib/math/base/special/gamma.h"
#include
int main( void ) {
const double x[] = { 4.0, -1.5, -0.5, 0.5 };
double y;
int i;
for ( i = 0; i < 4; i++ ) {
y = stdlib_base_gamma( x[ i ] );
printf( "gamma(%lf) = %lf\n", x[ i ], y );
}
}
`
*
See Also
- [@stdlib/math-base/special/gamma1pm1][@stdlib/math/base/special/gamma1pm1]: compute gamma(x+1) - 1.
- [@stdlib/math-base/special/gammainc][@stdlib/math/base/special/gammainc]: incomplete gamma function.
- [@stdlib/math-base/special/gammaincinv][@stdlib/math/base/special/gammaincinv]: inverse incomplete gamma function.
- [@stdlib/math-base/special/gammaln][@stdlib/math/base/special/gammaln]: natural logarithm of the gamma 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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[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-gamma
[test-image]: https://github.com/stdlib-js/math-base-special-gamma/actions/workflows/test.yml/badge.svg?branch=v0.3.1
[test-url]: https://github.com/stdlib-js/math-base-special-gamma/actions/workflows/test.yml?query=branch:v0.3.1
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-gamma/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-gamma?branch=main
[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[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-gamma/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-gamma/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-gamma/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-gamma/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-gamma/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-gamma/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-gamma/blob/main/branches.md
[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
[@stdlib/math/base/special/factorial]: https://www.npmjs.com/package/@stdlib/math-base-special-factorial
[real]: https://en.wikipedia.org/wiki/Real_number
[complex]: https://en.wikipedia.org/wiki/Complex_number
[@stdlib/constants/float64/eulergamma]: https://www.npmjs.com/package/@stdlib/constants-float64-eulergamma
[@stdlib/math/base/special/gamma1pm1]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma1pm1
[@stdlib/math/base/special/gammainc]: https://www.npmjs.com/package/@stdlib/math-base-special-gammainc
[@stdlib/math/base/special/gammaincinv]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaincinv
[@stdlib/math/base/special/gammaln]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaln