stdlib-js
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Gamma Scaled Lanczos Sum
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
Calculate a scaled Lanczos sum for the approximation of the [gamma function][gamma-function].
g is an [arbitrary constant][@stdlib/constants/float64/gamma-lanczos-g] and L_g(n) is the Lanczos sum. The scaled Lanczos sum is given by
bash
npm install @stdlib/math-base-special-gamma-lanczos-sum-expg-scaled
javascript
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][gamma-function] (scaled by exp(-g), where g = 10.900511).
javascript
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
javascript
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
#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][gamma-function] (scaled by exp(-g), where g = 10.900511).
c
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.
c
double stdlib_base_gamma_lanczos_sum_expg_scaled( const double x );
c
#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 );
}
}
@stdlib/math-base/special/gamma][@stdlib/math/base/special/gamma]: gamma function.
- [@stdlib/math-base/special/gamma-lanczos-sum][@stdlib/math/base/special/gamma-lanczos-sum]: calculate the Lanczos sum for the approximation of the gamma function.
