Gamma Scaled Lanczos Sum

Calculate a scaled 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. The scaled Lanczos sum is given by

Usage

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

gammaLanczosSumExpGScaled( x )

Calculates the Lanczos sum for the approximation of the gamma function (scaled by exp(-g), where g = 10.900511).

var v = gammaLanczosSumExpGScaled( 4.0 );
// returns ~0.018

v = gammaLanczosSumExpGScaled( -1.5 );
// returns ~25.337

v = gammaLanczosSumExpGScaled( -0.5 );
// returns ~-12.911

v = gammaLanczosSumExpGScaled( 0.5 );
// returns ~1.772

v = gammaLanczosSumExpGScaled( 0.0 );
// returns Infinity

v = gammaLanczosSumExpGScaled( NaN );
// returns NaN

Examples

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

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

C APIs

Usage

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

stdlib_base_gamma_lanczos_sum_expg_scaled( x )

Calculates the Lanczos sum for the approximation of the gamma function (scaled by exp(-g), where g = 10.900511).

double out = stdlib_base_gamma_lanczos_sum_expg_scaled( 4.0 );
// returns ~0.018

out = stdlib_base_gamma_lanczos_sum_expg_scaled( -1.5 );
// returns ~25.337

The function accepts the following arguments:

x: [in] double input value.

double stdlib_base_gamma_lanczos_sum_expg_scaled( const double x );

Examples

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