@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled

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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 ] ) );
}

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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.

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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

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Copyright

Copyright © 2016-2023. The Stdlib Authors.

Changelog

0.1.0 (2023-09-22)

<section class="features">

Features

• 58832ee - update minimum TypeScript version

</section> <!-- /.features --> <section class="breaking-changes">

BREAKING CHANGES

• 58832ee: update minimum TypeScript version to 4.1

  • To migrate, users should upgrade their TypeScript version to at least version 4.1.

</section> <!-- /.breaking-changes --> <section class="commits">

Commits

<details>

• 58832ee - feat: update minimum TypeScript version (by Philipp Burckhardt)
• a37ebe2 - docs: remove empty lines (by Philipp Burckhardt)
• b734544 - refactor: use strictEqual checks (by Philipp Burckhardt)
• c5da1f9 - docs: render equations via math code blocks (by Philipp Burckhardt)

</details> </section> <!-- /.commits --> <section class="contributors">

Contributors

A total of 1 person contributed to this release. Thank you to this contributor:

• Philipp Burckhardt

</section> <!-- /.contributors --> </section> <!-- /.release --> <section class="release" id="v0.0.7">