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https://github.com/stdlib-js/math-base-special-polygamma
Polygamma function.
https://github.com/stdlib-js/math-base-special-polygamma
derivative gamma javascript math mathematics node node-js nodejs number polygamma psi scalar special-function stdlib
Last synced: 15 days ago
JSON representation
Polygamma function.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-polygamma
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:31:58.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-10-01T12:59:24.000Z (about 1 month ago)
- Last Synced: 2024-10-09T19:32:19.870Z (27 days ago)
- Topics: derivative, gamma, javascript, math, mathematics, node, node-js, nodejs, number, polygamma, psi, scalar, special-function, stdlib
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 1.83 MB
- Stars: 3
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
Awesome Lists containing this project
README
About stdlib...
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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!
# Polygamma
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Polygamma][polygamma-function] function.
## Installation
```bash
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][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] 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
```javascript
var polygamma = require( '@stdlib/math-base-special-polygamma' );
```
#### polygamma( n, x )
Evaluates the [polygamma function][polygamma-function] of order `n`; i.e., the `(n+1)`th derivative of the [natural logarithm][@stdlib/math/base/special/ln] of the [gamma function][@stdlib/math/base/special/gamma].
```javascript
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`.
```javascript
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`.
```javascript
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`.
```javascript
v = polygamma( 2, -4.0 );
// returns NaN
v = polygamma( 2, -2.0 );
// returns NaN
```
If provided `NaN` as either parameter, the function returns `NaN`.
```javascript
var v = polygamma( NaN, 2.1 );
// returns NaN
v = polygamma( 1, NaN );
// returns NaN
v = polygamma( NaN, NaN );
// returns NaN
```
## Examples
```javascript
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
- [`@stdlib/math-base/special/trigamma`][@stdlib/math/base/special/trigamma]: trigamma function.
- [`@stdlib/math-base/special/digamma`][@stdlib/math/base/special/digamma]: digamma function.
- [`@stdlib/math-base/special/gamma`][@stdlib/math/base/special/gamma]: gamma function.
* * *
## 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]
---
## Copyright
Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-polygamma.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-polygamma
[test-image]: https://github.com/stdlib-js/math-base-special-polygamma/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-polygamma/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-polygamma/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-polygamma?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[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-polygamma/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-polygamma/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-polygamma/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-polygamma/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-polygamma/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-polygamma/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-polygamma/blob/main/branches.md
[polygamma-function]: https://en.wikipedia.org/wiki/Polygamma_function
[@stdlib/math/base/special/ln]: https://github.com/stdlib-js/math-base-special-ln
[@stdlib/math/base/special/trigamma]: https://github.com/stdlib-js/math-base-special-trigamma
[@stdlib/math/base/special/digamma]: https://github.com/stdlib-js/math-base-special-digamma
[@stdlib/math/base/special/gamma]: https://github.com/stdlib-js/math-base-special-gamma