Define Hermite polynomials

[mcdoll]

What the title says. We already have Chebychev polynomials and Bernstein polynomials, which could serve as a guide.
Showing that the Hermite polynomials form a basis of L^2 would a great way to continue this project, but this is more involved.

[achobani]

Hi, I would be interested in working on this!

[mcdoll]

#18739