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https://github.com/stdlib-js/math-base-special-falling-factorial

Compute the falling factorial.
https://github.com/stdlib-js/math-base-special-falling-factorial

descending factorial falling falling-sequential function gamma javascript lower math mathematics node node-js nodejs number special special-function stdlib

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Compute the falling factorial.

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README 

        



  

    About stdlib...

  

  
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# Falling Factorial



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Compute the [falling factorial][falling-and-rising-factorials].



## Installation



```bash

npm install @stdlib/math-base-special-falling-factorial

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## Usage



```javascript

var fallingFactorial = require( '@stdlib/math-base-special-falling-factorial' );

```



#### fallingFactorial( x, n )



Evaluates the [falling factorial][falling-and-rising-factorials] of `x` and `n`.



```javascript

var v = fallingFactorial( 0.9, 5 );

// returns ~0.644



v = fallingFactorial( -9.0, 3 );

// returns -990.0



v = fallingFactorial( 0.0, 2 );

// returns 0.0



v = fallingFactorial( NaN, 3 );

// returns NaN



v = fallingFactorial( 5.0, NaN );

// returns NaN



v = fallingFactorial( NaN, NaN );

// returns NaN

```



The function returns `NaN` if not provided a nonnegative integer for `n`.



```javascript

var v = fallingFactorial( 2.0, 1.5 );

// returns NaN



v = fallingFactorial( 3.0, -2 );

// returns NaN

```



## Examples



```javascript

var randu = require( '@stdlib/random-array-uniform' );

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );

var fallingFactorial = require( '@stdlib/math-base-special-falling-factorial' );



var x = randu( 100, -20.0, 20.0 );

var n = discreteUniform( 100, 0, 20 );



var i;

for ( i = 0; i < 100; i++ ) {

    console.log( 'fallingFactorial(%d,%d) = %d', x[ i ], n[ i ], fallingFactorial( x[ i ], n[ i ] ) );

}

```



* * *



## C APIs



### Usage



```c

#include "stdlib/math/base/special/falling_factorial.h"

```



#### stdlib_base_falling_factorial( x, n )



Evaluates the [falling factorial][falling-and-rising-factorials] of `x` and `n`.



```c

double out = stdlib_base_falling_factorial( 0.9, 5 );

// returns ~0.644



out = stdlib_base_falling_factorial( -9.0, 3 );

// returns -990.0

```



The function accepts the following arguments:



-   **x**: `[in] double` first function parameter.

-   **n**: `[in] int32_t` second function parameter.



```c

double stdlib_base_falling_factorial( const double x, const int32_t n );

```



### Examples



```c

#include "stdlib/math/base/special/falling_factorial.h"

#include 

#include 



int main( void ) {

    const double x[] = { -10.0, -7.78, -5.56, -3.33, -1.11, 1.11, 3.33, 5.56, 7.78, 10.0 };

    const int32_t n[] = { 5, 4, 3, 2, 1, 0, -1, -2, -3, -4 };



    double v;

    int i;

    for ( i = 0; i < 10; i++ ) {

        v = stdlib_base_falling_factorial( x[ i ], n[ i ] );

        printf( "x: %lf, n: %d, falling_factorial(x,n): %lf\n", x[ i ], n[ i ], v );

    }

}

```



* * *



## See Also



-   [`@stdlib/math-base/special/rising-factorial`][@stdlib/math/base/special/rising-factorial]: compute the rising factorial.



* * *



## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-falling-factorial.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-falling-factorial



[test-image]: https://github.com/stdlib-js/math-base-special-falling-factorial/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-base-special-falling-factorial/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-falling-factorial/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-falling-factorial?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[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-falling-factorial/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-base-special-falling-factorial/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-base-special-falling-factorial/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-base-special-falling-factorial/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-base-special-falling-factorial/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-base-special-falling-factorial/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-base-special-falling-factorial/blob/main/branches.md



[falling-and-rising-factorials]: https://en.wikipedia.org/wiki/Falling_and_rising_factorials



[@stdlib/math/base/special/rising-factorial]: https://github.com/stdlib-js/math-base-special-rising-factorial