Gamma Function
Gamma function.
The gamma function extends the factorial function to real and complex numbers. If n is a positive integer,
Generalized to all complex numbers z, except for nonpositive integers, the gamma function can be expressed as an infinite product
where γ ≈ 0.577216 is the Euler–Mascheroni constant.
Usage
var gamma = require( '@stdlib/math/base/special/gamma' );
gamma( x )
Evaluates the gamma function.
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
var linspace = require( '@stdlib/array/base/linspace' );
var gamma = require( '@stdlib/math/base/special/gamma' );
var x = linspace( -10.0, 10.0, 100 );
var i;
for ( i = 0; i < x.length; i++ ) {
console.log( 'x: %d, f(x): %d', x[ i ], gamma( x[ i ] ) );
}
C APIs
Usage
#include "stdlib/math/base/special/gamma.h"
stdlib_base_gamma( x )
Evaluates the gamma function.
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] doubleinput value.
double stdlib_base_gamma( const double x );
Examples
#include "stdlib/math/base/special/gamma.h"
#include <stdio.h>
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 );
}
}