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Factorial

Factorial function.

The factorial function may be defined as the product

Factorial function definition

or according to the recurrence relation

Factorial function recurrence relation

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

Zero factorial

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

Factorial function extension via the Gamma function

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/array/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 );
}