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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 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:

$$\Gamma ( n ) = \frac{(n+g-0.5)^{n-0.5}}{e^{n+g-0.5}} L_g(n)$$

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

$$L_g(n) \cdot \exp(-g)$$

Usage

import gammaLanczosSumExpGScaled from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-gamma-lanczos-sum-expg-scaled@deno/mod.js';

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

import linspace from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-base-linspace@deno/mod.js';
import gammaLanczosSumExpGScaled from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-gamma-lanczos-sum-expg-scaled@deno/mod.js';

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 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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