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    @stdlib/math-base-special-gamma-lanczos-sum-expg-scaled
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    0.0.7 • Public • Published

    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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    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

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

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    5,409

    Version

    0.0.7

    License

    Apache-2.0 AND BSL-1.0

    Unpacked Size

    57.3 kB

    Total Files

    12

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    Collaborators

    • stdlib-bot
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