Gamma Lanczos Sum

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.

Installation

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

Usage

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

gammaLanczosSum( x )

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

Examples

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 APIs

Usage

#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.

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.

double stdlib_base_gamma_lanczos_sum( const double x );

Examples

#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 );
    }
}

See Also

• @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.

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.