Gamma Scaled Lanczos Sum

Calculate a scaled Lanczos sum for the approximation of the gamma function as a single precision floating-point number.

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-scaledf

Usage

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

gammaLanczosSumExpGScaledf( x )

Calculates the Lanczos sum for the approximation of the gamma function (scaled by exp(-g), where g = 1.42845618724823) as a single precision floating-point number.

var v = gammaLanczosSumExpGScaledf( 4.0 );
// returns ~0.748

v = gammaLanczosSumExpGScaledf( -1.5 );
// returns ~0.193

v = gammaLanczosSumExpGScaledf( -0.5 );
// returns ~-0.558

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

v = gammaLanczosSumExpGScaledf( 0.0 );
// returns Infinity

v = gammaLanczosSumExpGScaledf( NaN );
// returns NaN

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var gammaLanczosSumExpGScaledf = require( '@stdlib/math-base-special-gamma-lanczos-sum-expg-scaledf' );

var opts = {
    'dtype': 'float32'
};
var x = uniform( 100, -10.0, 10.0, opts );

logEachMap( 'x: %0.4f, f(x): %0.4f', x, gammaLanczosSumExpGScaledf );

C APIs

Usage

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

stdlib_base_gamma_lanczos_sum_expg_scaledf( x )

Calculates the Lanczos sum for the approximation of the gamma function (scaled by exp(-g), where g = 1.42845618724823) as a single precision floating-point number.

float out = stdlib_base_gamma_lanczos_sum_expg_scaledf( 4.0f );
// returns ~0.748f

out = stdlib_base_gamma_lanczos_sum_expg_scaledf( -1.5f );
// returns ~0.193f

The function accepts the following arguments:

• x: [in] float input value.

float stdlib_base_gamma_lanczos_sum_expg_scaledf( const float x );

Examples

#include "stdlib/math/base/special/gamma_lanczos_sum_expg_scaledf.h"
#include <stdio.h>

int main( void ) {
    const float x[] = { 4.0f, -1.5f, -0.5f, 0.5f };

    float y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_gamma_lanczos_sum_expg_scaledf( x[ i ] );
        printf( "gamma_lanczos_sum_expg_scaledf(%f) = %f\n", x[ i ], y );
    }
}

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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