stdlib-js
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Gamma Lanczos Sum
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Calculate the 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.
bash
npm install @stdlib/math-base-special-gamma-lanczos-sum
javascript
var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );
#### gammaLanczosSum( x )
Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].
javascript
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
javascript
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
#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][gamma-function].
c
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.
c
double stdlib_base_gamma_lanczos_sum( const double x );
c
#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 );
}
}
@stdlib/math-base/special/gamma][@stdlib/math/base/special/gamma]: gamma function.
- [@stdlib/math-base/special/gamma-lanczos-sum-expg-scaled][@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled]: calculate a scaled Lanczos sum for the approximation of the gamma function.
