@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled v0.2.1
Gamma Scaled Lanczos Sum
Calculate a scaled 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. The scaled Lanczos sum is given by
Installation
npm install @stdlib/math-base-special-gamma-lanczos-sum-expg-scaled
Usage
var gammaLanczosSumExpGScaled = require( '@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled' );
gammaLanczosSumExpGScaled( x )
Calculates the Lanczos sum for the approximation of the gamma function (scaled by exp(-g)
, where g = 10.900511
).
var v = gammaLanczosSumExpGScaled( 4.0 );
// returns ~0.018
v = gammaLanczosSumExpGScaled( -1.5 );
// returns ~25.337
v = gammaLanczosSumExpGScaled( -0.5 );
// returns ~-12.911
v = gammaLanczosSumExpGScaled( 0.5 );
// returns ~1.772
v = gammaLanczosSumExpGScaled( 0.0 );
// returns Infinity
v = gammaLanczosSumExpGScaled( NaN );
// returns NaN
Examples
var linspace = require( '@stdlib/array-base-linspace' );
var gammaLanczosSumExpGScaled = require( '@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled' );
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 ], gammaLanczosSumExpGScaled( x[ i ] ) );
}
See Also
@stdlib/math-base/special/gamma
: gamma function.@stdlib/math-base/special/gamma-lanczos-sum
: calculate the 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
Copyright
Copyright © 2016-2024. The Stdlib Authors.
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