how can I expand a real function by hermite polinomials?

How can I expand a monovariable function by Hermite polinomials?

Answer 1

[John D'Errico]

In the obvious way? :)

Hermite polynomials form an orthogonal set of functions over a specific domain, with a given weight function. A basis set. So you could form the indicated dot products to gain coefficients to be applied to the Hermite polynomials. You will create an expansion for your function as a linear combination of Hermite polynomials.