hermiteh.m : Hn(x), a hermite polynomial calculator

Version 1.3.0.0 (740 Bytes) by Shawn Divitt
Returns the value of the nth Hermite polynomial of x.
0.0
(0)
716 Downloads
Updated 3 Nov 2014

View License

This function returns the value of the nth Hermite polynomial of x. It is defined in terms of the "physicists" Hermite polynomials (see Wikipedia).
Syntax: val = hermiteh(n,x);
Where "n" is the order of the polynomial and "x" is the argument. "x" can be a scalar or an array with up to two dimensions.
Also included is an example script to show one possible use. The image displayed with this file is of the Hermite-Gaussian 3,3 mode and uses hermiteh.m to create it.

This function is expected to be a bit faster for high orders than the submission acknowledged below because it uses the explicit formula and not the recursion relation.

Cite As

Shawn Divitt (2026). hermiteh.m : Hn(x), a hermite polynomial calculator (https://www.mathworks.com/matlabcentral/fileexchange/47725-hermiteh-m-hn-x-a-hermite-polynomial-calculator), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Polynomials in Help Center and MATLAB Answers
Tags Add Tags
Acknowledgements

Inspired by: Hermite polynomials

Open in new tab
Version Published Release Notes
1.3.0.0

The example script was missing a sqrt(2) scaling factor and as a result gave the wrong distribution for the Hermite-Gaussian modes. This change does not affect the calculator itself. Updated to the correct picture of the Hermite-Gaussian 3,3 mode.
1.2.0.0

updated title
1.1.0.0

rev. 1 - added an example script and an image
1.0.0.0