Polygamma

Polygamma function.

Installation

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

Alternatively,

To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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 );
}

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.