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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 );
}