@stdlib/math-base-special-gamma-lanczos-sum
v0.2.1
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Calculate the Lanczos sum for the approximation of the gamma function.
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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.
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 ] ) );
}
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.
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License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.