# @stdlib/math-base-tools-normhermitepoly

0.2.1 • Public • Published

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# Normalized Hermite Polynomial

Evaluate a normalized Hermite polynomial.

The normalized (aka "probabilist") Hermite polynomials are given by

## Installation

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

## Usage

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

#### normhermitepoly( n, x )

Evaluates a normalized Hermite polynomial of degree `n`.

```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 of degree `n`.

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

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

## Examples

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

var xx;
var yy;
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 = normhermitepoly( j, x );
xx = x.toFixed(3);
yy = y.toFixed(3);
console.log( 'He_%d( %d ) = %d', j, xx, yy );
}
}```

## 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.

## Package Sidebar

### Install

`npm i @stdlib/math-base-tools-normhermitepoly`

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