About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Gamma Lanczos Sum

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Calculate the Lanczos sum for the approximation of the [gamma function][gamma-function].

The [Lanczos approximation][lanczos-approximation] for the [gamma function][gamma-function] can be written in partial fraction form as follows:

$Lanczos approximation for gamma function.$

where g is an [arbitrary constant][@stdlib/constants/float64/gamma-lanczos-g] and L_g(n) is the Lanczos sum.

Installation

``bash npm install @stdlib/math-base-special-gamma-lanczos-sum`

`Usage`

`javascript var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );`

#### gammaLanczosSum( x )

Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].

`javascript 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`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );

var opts = { 'dtype': 'float64' }; var x = uniform( 100, -10.0, 10.0, opts );

logEachMap( 'x: %0.4f, f(x): %0.4f', x, gammaLanczosSum );`

*

`C APIs`

`$3`

`c #include "stdlib/math/base/special/gamma_lanczos_sum.h"`

#### stdlib_base_gamma_lanczos_sum( x )

Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].

`c double out = stdlib_base_gamma_lanczos_sum( 4.0 ); // returns ~950.366

out = stdlib_base_gamma_lanczos_sum( -1.5 ); // returns ~1373366.245`

The function accepts the following arguments:

- x: [in] double input value.

`c double stdlib_base_gamma_lanczos_sum( const double x );`

`$3`

`c #include "stdlib/math/base/special/gamma_lanczos_sum.h" #include #include

int main( void ) { const double x[] = { 4.0, -1.5, -0.5, 0.5 };

double y; int i; for ( i = 0; i < 4; i++ ) { y = stdlib_base_gamma_lanczos_sum( x[ i ] ); printf( "gamma_lanczos_sum(%lf) = %lf\n", x[ i ], y ); } }`

*

`Notice`

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-gamma-lanczos-sum.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-special-gamma-lanczos-sum

[test-image]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/actions/workflows/test.yml/badge.svg?branch=v0.3.2 [test-url]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/actions/workflows/test.yml?query=branch:v0.3.2

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-gamma-lanczos-sum/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-gamma-lanczos-sum?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/tree/deno [deno-readme]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/tree/umd [umd-readme]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/tree/esm [esm-readme]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/math-base-special-gamma-lanczos-sum/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-gamma-lanczos-sum/main/LICENSE

[@stdlib/constants/float64/gamma-lanczos-g]: https://www.npmjs.com/package/@stdlib/constants-float64-gamma-lanczos-g

[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function

[lanczos-approximation]: https://en.wikipedia.org/wiki/Lanczos_approximation

[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma

[@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma-lanczos-sum-expg-scaled


  
    About stdlib...
  

  We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

  The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

  When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`Gamma Lanczos Sum`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Calculate the Lanczos sum for the approximation of the [gamma function][gamma-function].

The [Lanczos approximation][lanczos-approximation] for the [gamma function][gamma-function] can be written in partial fraction form as follows:

where g is an [arbitrary constant][@stdlib/constants/float64/gamma-lanczos-g] and L_g(n) is the Lanczos sum.

`Installation`

``bash npm install @stdlib/math-base-special-gamma-lanczos-sum `

`Usage`

`javascript var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' ); `

#### gammaLanczosSum( x )

Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].

`javascript 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`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var gammaLanczosSum = require( '@stdlib/math-base-special-gamma-lanczos-sum' );

var opts = { 'dtype': 'float64' }; var x = uniform( 100, -10.0, 10.0, opts );

logEachMap( 'x: %0.4f, f(x): %0.4f', x, gammaLanczosSum ); `

*

`C APIs`

`$3`

`c #include "stdlib/math/base/special/gamma_lanczos_sum.h" `

#### stdlib_base_gamma_lanczos_sum( x )

Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function].

`c double out = stdlib_base_gamma_lanczos_sum( 4.0 ); // returns ~950.366

out = stdlib_base_gamma_lanczos_sum( -1.5 ); // returns ~1373366.245 `

The function accepts the following arguments:

- x: [in] double input value.

`c double stdlib_base_gamma_lanczos_sum( const double x ); `

`$3`

`c #include "stdlib/math/base/special/gamma_lanczos_sum.h" #include #include

int main( void ) { const double x[] = { 4.0, -1.5, -0.5, 0.5 };

double y; int i; for ( i = 0; i < 4; i++ ) { y = stdlib_base_gamma_lanczos_sum( x[ i ] ); printf( "gamma_lanczos_sum(%lf) = %lf\n", x[ i ], y ); } } `