Gamma Lanczos Sum

Calculate the Lanczos sum for the approximation of the gamma function.

The Lanczos approximation for the gamma function can be written in partial fraction form as follows:

where g is an arbitrary constant and L_g(n) is the Lanczos sum.

Usage

var gammaLanczosSum = require( '@stdlib/math/base/special/gamma-lanczos-sum' );

gammaLanczosSum( x )

Calculates the Lanczos sum for the approximation of the gamma function.

var v = gammaLanczosSum( 4.0 );
// returns ~950.366

v = gammaLanczosSum( -1.5 );
// returns ~1373366.245

v = gammaLanczosSum( -0.5 );
// returns ~-699841.735

v = gammaLanczosSum( 0.5 );
// returns ~96074.186

v = gammaLanczosSum( 0.0 );
// returns Infinity

v = gammaLanczosSum( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/array/base/linspace' );
var gammaLanczosSum = require( '@stdlib/math/base/special/gamma-lanczos-sum' );

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 ], gammaLanczosSum( x[ i ] ) );
}

C APIs

Usage

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

stdlib_base_gamma_lanczos_sum( x )

Calculates the Lanczos sum for the approximation of the gamma function.

double out = stdlib_base_gamma_lanczos_sum( 4.0 );
// returns ~950.366

out = stdlib_base_gamma_lanczos_sum( -1.5 );
// returns ~1373366.245

The function accepts the following arguments:

x: [in] double input value.

double stdlib_base_gamma_lanczos_sum( const double x );

Examples

#include "stdlib/math/base/special/gamma_lanczos_sum.h"
#include <stdlib.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_lanczos_sum( x[ i ] );
        printf( "gamma_lanczos_sum(%lf) = %lf\n", x[ i ], y );
    }
}