Factorial

Factorial function.

The factorial function may be defined as the product

n factorial equals product Underscript k equals 1 Overscript n Endscripts k

or according to the recurrence relation

n factorial equals StartLayout Enlarged left-brace 1st Row 1st Column 1 2nd Column if n equals 0 comma 2nd Row 1st Column left-parenthesis n minus 1 right-parenthesis factorial times n 2nd Column if n greater-than 1 EndLayout

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

0 factorial equals 1

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

n factorial equals normal upper Gamma left-parenthesis n plus 1 right-parenthesis

The factorial of a negative integer is not defined.

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

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

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