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!

Normalized Hermite Polynomial

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Evaluate a normalized [Hermite polynomial][hermite-polynomial] using double-precision floating-point arithmetic.

The normalized (aka "probabilist") [Hermite polynomials][hermite-polynomial] are given by

$Equation for normalized Hermite polynomials.$

Installation

``bash npm install @stdlib/math-base-tools-normhermitepoly`

`Usage`

`javascript var normhermitepoly = require( '@stdlib/math-base-tools-normhermitepoly' );`

#### normhermitepoly( n, x )

Evaluates a normalized [Hermite polynomial][hermite-polynomial] of degree n using double-precision floating-point arithmetic.

`javascript var v = normhermitepoly( 1, 1.0 ); // returns 1.0

v = normhermitepoly( 1, 0.5 ); // returns 0.5

v = normhermitepoly( 0, 0.5 ); // returns 1.0

v = normhermitepoly( 2, 0.5 ); // returns -0.75

v = normhermitepoly( -1, 0.5 ); // returns NaN`

#### normhermitepoly.factory( n )

Returns a function for evaluating a normalized [Hermite polynomial][hermite-polynomial] of degree n using double-precision floating-point arithmetic.

`javascript var polyval = normhermitepoly.factory( 2 );

var v = polyval( 0.5 ); // returns -0.75`

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var zeros = require( '@stdlib/array-zeros' ); var dmap = require( '@stdlib/strided-base-dmap' ); var logEach = require( '@stdlib/console-log-each' ); var normhermitepoly = require( '@stdlib/math-base-tools-normhermitepoly' );

// Generate random values at which to evaluate a polynomial: var x = uniform( 10, -50.0, 50.0, { 'dtype': 'float64' });

// Create a polynomial function of degree 1: var f = normhermitepoly.factory( 1 );

// Allocate an output array: var y = zeros( x.length, 'float64' );

// Evaluate the polynomial: dmap( x.length, x, 1, y, 1, f ); logEach( 'He_%d(%.3f) = %.3f', 1, x, y );

// Create a polynomial function of degree 2: f = normhermitepoly.factory( 2 );

// Allocate an output array: y = zeros( x.length, 'float64' );

// Evaluate the polynomial: dmap( x.length, x, 1, y, 1, f ); logEach( 'He_%d(%.3f) = %.3f', 2, x, y );

// Create a polynomial function of degree 3: f = normhermitepoly.factory( 3 );

// Allocate an output array: y = zeros( x.length, 'float64' );

// Evaluate the polynomial: dmap( x.length, x, 1, y, 1, f ); logEach( 'He_%d(%.3f) = %.3f', 3, x, y );`

*

`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]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-tools-normhermitepoly.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-normhermitepoly

[test-image]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/actions/workflows/test.yml/badge.svg?branch=v0.2.3 [test-url]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/actions/workflows/test.yml?query=branch:v0.2.3

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-normhermitepoly/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-normhermitepoly?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[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-tools-normhermitepoly/tree/deno [deno-readme]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/tree/umd [umd-readme]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/tree/esm [esm-readme]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/math-base-tools-normhermitepoly/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-normhermitepoly/main/LICENSE

[hermite-polynomial]: https://en.wikipedia.org/wiki/Hermite_polynomials

[@stdlib/math/base/tools/evalpoly]: https://www.npmjs.com/package/@stdlib/math-base-tools-evalpoly

[@stdlib/math/base/tools/hermitepoly]: https://www.npmjs.com/package/@stdlib/math-base-tools-hermitepoly


  
    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!

`Normalized Hermite Polynomial`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Evaluate a normalized [Hermite polynomial][hermite-polynomial] using double-precision floating-point arithmetic.

The normalized (aka "probabilist") [Hermite polynomials][hermite-polynomial] are given by

`Installation`

``bash npm install @stdlib/math-base-tools-normhermitepoly `

`Usage`

`javascript var normhermitepoly = require( '@stdlib/math-base-tools-normhermitepoly' ); `

#### normhermitepoly( n, x )

Evaluates a normalized [Hermite polynomial][hermite-polynomial] of degree n using double-precision floating-point arithmetic.

`javascript var v = normhermitepoly( 1, 1.0 ); // returns 1.0

v = normhermitepoly( 1, 0.5 ); // returns 0.5

v = normhermitepoly( 0, 0.5 ); // returns 1.0

v = normhermitepoly( 2, 0.5 ); // returns -0.75

v = normhermitepoly( -1, 0.5 ); // returns NaN `

#### normhermitepoly.factory( n )

Returns a function for evaluating a normalized [Hermite polynomial][hermite-polynomial] of degree n using double-precision floating-point arithmetic.

`javascript var polyval = normhermitepoly.factory( 2 );

var v = polyval( 0.5 ); // returns -0.75 `

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var zeros = require( '@stdlib/array-zeros' ); var dmap = require( '@stdlib/strided-base-dmap' ); var logEach = require( '@stdlib/console-log-each' ); var normhermitepoly = require( '@stdlib/math-base-tools-normhermitepoly' );