@stdlib/math-base-tools-hermitepoly
v0.2.3TypeScript
Evaluate a physicist's Hermite polynomial.
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Published by The Stdlib Authors
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Physicist's Hermite Polynomial
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> Evaluate a physicist's [Hermite polynomial][hermite-polynomial].
The physicist's [Hermite polynomials][hermite-polynomial] are given by
Installation
``bash`
npm install @stdlib/math-base-tools-hermitepoly
Usage
`javascript`
var hermitepoly = require( '@stdlib/math-base-tools-hermitepoly' );
#### hermitepoly( n, x )
Evaluates a physicist's [Hermite polynomial][hermite-polynomial] of degree n.
`javascript
var v = hermitepoly( 1, 1.0 );
// returns 2.0
v = hermitepoly( 1, 0.5 );
// returns ~1.0
v = hermitepoly( -1, 0.5 );
// returns NaN
v = hermitepoly( 0, 0.5 );
// returns 1.0
v = hermitepoly( 2, 0.5 );
// returns -1.0
`
#### hermitepoly.factory( n )
Returns a function for evaluating a physicist's [Hermite polynomial][hermite-polynomial] of degree n.
`javascript
var polyval = hermitepoly.factory( 2 );
var v = polyval( 0.5 );
// returns -1.0
`
Examples
`javascript
var randu = require( '@stdlib/random-base-randu');
var hermitepoly = require( '@stdlib/math-base-tools-hermitepoly' );
var x;
var y;
var i;
var j;
for ( i = 0; i < 100; i++ ) {
x = (randu()*100.0) - 50.0;
for ( j = 1; j < 3; j++ ) {
y = hermitepoly( j, x );
console.log( 'H_%d( %d ) = %d', j, x.toFixed( 3 ), y.toFixed( 3 ) );
}
}
`
*
See Also
- [@stdlib/math-base/tools/evalpoly][@stdlib/math/base/tools/evalpoly]: evaluate a polynomial using double-precision floating-point arithmetic.
- [@stdlib/math-base/tools/normhermitepoly][@stdlib/math/base/tools/normhermitepoly]: evaluate a normalized Hermite polynomial using double-precision floating-point arithmetic.
*
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
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-hermitepoly
[test-image]: https://github.com/stdlib-js/math-base-tools-hermitepoly/actions/workflows/test.yml/badge.svg?branch=v0.2.3
[test-url]: https://github.com/stdlib-js/math-base-tools-hermitepoly/actions/workflows/test.yml?query=branch:v0.2.3
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-hermitepoly/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-hermitepoly?branch=main
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[stdlib]: https://github.com/stdlib-js/stdlib
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[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-hermitepoly/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-tools-hermitepoly/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-tools-hermitepoly/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-tools-hermitepoly/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-tools-hermitepoly/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-tools-hermitepoly/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-tools-hermitepoly/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-hermitepoly/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/normhermitepoly]: https://www.npmjs.com/package/@stdlib/math-base-tools-normhermitepoly