@stdlib/math-base-special-gamma-lanczos-sum
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Calculate the Lanczos sum for the approximation of the gamma function.
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Calculate the 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.
npm install @stdlib/math-base-special-gamma-lanczos-sum
var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );
Calculates the Lanczos sum for the approximation of the gamma function.
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
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 ] ) );
}
#include "stdlib/math/base/special/gamma_lanczos_sum.h"
Calculates the Lanczos sum for the approximation of the gamma function.
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:
[in] double input value.double stdlib_base_gamma_lanczos_sum( const double x );
#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: gamma function.@stdlib/math-base/special/gamma-lanczos-sum-expg-scaled: calculate a scaled Lanczos sum for the approximation of the gamma function.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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.
0.3.0 (2024-07-27)
<section class="features">This release closes the following issue:
</section> <!-- /.issues --> <section class="commits">53eb98c - docs: fix function name (#2579) (by Gunj Joshi)2789eff - docs: fix function name in README example (#2506) (by Gunj Joshi)f36cfab - chore: update package meta data (#2014) (by stdlib-bot)5c8ab25 - feat: add C implementation for math/base/special/gamma-lanczos-sum (#1834) (by Gunj Joshi, Athan Reines)A total of 2 people contributed to this release. Thank you to the following contributors:
FAQs
Calculate the Lanczos sum for the approximation of the gamma function.
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