time-to-botec/js/node_modules/@stdlib/math/base/special/gamma-lanczos-sum

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.

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

var x = linspace( -10.0, 10.0, 100 );
var v;
var i;

for ( i = 0; i < x.length; i++ ) {
    v = gammaLanczosSum( x[ i ] );
    console.log( 'x: %d, f(x): %d', x[ i ], v );
}