factorial

Factorial function.

The factorial function may be defined as the product

or according to the recurrence relation

Following the convention for an empty product, in all definitions,

The Gamma function extends the factorial function for non-integer values.

The factorial of a negative integer is not defined.

Installation

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

Usage

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

factorial( x )

Evaluates the factorial function.

var v = factorial( 3.0 );
// returns 6.0

v = factorial( -1.5 );
// returns ~-3.545

v = factorial( -0.5 );
// returns ~1.772

v = factorial( 0.5 );
// returns ~0.886

v = factorial( -10.0 );
// returns NaN

v = factorial( 171.0 );
// returns Infinity

v = factorial( NaN );
// returns NaN

Examples

var incrspace = require( '@stdlib/array-base-incrspace' );
var factorial = require( '@stdlib/math-base-special-factorial' );

var x = incrspace( -10.0, 100.0, 1.0 );

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

C APIs

Usage

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

stdlib_base_factorial( x )

Evaluates the factorial function.

double out = stdlib_base_factorial( 3.0 );
// returns 6.0

out = stdlib_base_factorial( -1.5 );
// returns ~-3.545

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_factorial( const double n );

Examples

#include "stdlib/math/base/special/factorial.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 2.0, 3.0, 5.0, 8.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_factorial( x[ i ] );
        printf( "factorial(%lf) = %lf\n", x[ i ], y );
    }
}

See Also

• @stdlib/math-base/special/factorialln: evaluate the natural logarithm of the factorial function.

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.