@stdlib/math-base-special-polygamma
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    0.0.6 • Public • Published

    Polygamma

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    Polygamma function.

    Installation

    npm install @stdlib/math-base-special-polygamma

    Usage

    var polygamma = require( '@stdlib/math-base-special-polygamma' );

    polygamma( n, x )

    Evaluates the polygamma function of order n; i.e., the (n+1)th derivative of the natural logarithm of the gamma function.

    var v = polygamma( 3, 1.2 );
    // returns ~3.245
    
    v = polygamma( 5, 1.2 );
    // returns ~41.39
    
    v = polygamma( 3, -4.9 );
    // returns ~60014.239

    If n is not a nonnegative integer, the function returns NaN.

    var v = polygamma( 2.5, -1.2 );
    // returns NaN
    
    v = polygamma( -1, 5.3 );
    // returns NaN

    If x is 0 or a negative odd integer, the function returns +Infinity.

    var v = polygamma( 2, 0.0 );
    // returns +Infinity
    
    v = polygamma( 2, -1.0 );
    // returns +Infinity

    If x on the other hand is a negative even integer, the function returns NaN.

    v = polygamma( 2, -4.0 );
    // returns NaN
    
    v = polygamma( 2, -2.0 );
    // returns NaN

    If provided NaN as either parameter, the function returns NaN.

    var v = polygamma( NaN, 2.1 );
    // returns NaN
    
    v = polygamma( 1, NaN );
    // returns NaN
    
    v = polygamma( NaN, NaN );
    // returns NaN

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var polygamma = require( '@stdlib/math-base-special-polygamma' );
    
    var n;
    var x;
    var v;
    var i;
    
    for ( i = 0; i < 100; i++ ) {
        x = (randu()*100.0) - 50.0;
        n = round( randu()*50.0 );
        v = polygamma( x, n );
        console.log( 'x: %d, ψ^(%d)(x): %d', x, n, v );
    }

    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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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/math-base-special-polygamma

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    34

    Version

    0.0.6

    License

    Apache-2.0 AND BSL-1.0

    Unpacked Size

    75.9 kB

    Total Files

    23

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser