Physicist's Hermite Polynomial

Evaluate a physicist's Hermite polynomial.

The physicist's Hermite polynomials are given by

Installation

npm install @stdlib/math-base-tools-hermitepoly

Usage

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

hermitepoly( n, x )

Evaluates a physicist's Hermite polynomial of degree n.

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 of degree n.

var polyval = hermitepoly.factory( 2 );

var v = polyval( 0.5 );
// returns -1.0

Examples

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: evaluate a polynomial using double-precision floating-point arithmetic.
• @stdlib/math-base/tools/normhermitepoly: evaluate a normalized Hermite polynomial using double-precision floating-point arithmetic.

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.