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Calculate a scaled Lanczos sum for the approximation of the gamma function.

Package Exports

  • @stdlib/math-base-special-gamma-lanczos-sum-expg-scaled
  • @stdlib/math-base-special-gamma-lanczos-sum-expg-scaled/lib/index.js

This package does not declare an exports field, so the exports above have been automatically detected and optimized by JSPM instead. If any package subpath is missing, it is recommended to post an issue to the original package (@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled) to support the "exports" field. If that is not possible, create a JSPM override to customize the exports field for this package.

Readme

Gamma Scaled Lanczos Sum

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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:

Lanczos approximation for gamma function.

where g is an arbitrary constant and L_g(n) is the Lanczos sum. The scaled Lanczos sum is given by

Scaled Lanczos sum.

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

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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