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

Installation

npm install @stdlib/math-base-special-gamma-lanczos-sum-expg-scaled

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 );
    }
}

See Also

• @stdlib/math-base/special/gamma: gamma function.
• @stdlib/math-base/special/gamma-lanczos-sum: calculate the Lanczos sum for the approximation of the gamma function.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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Copyright

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