Open AccessOperational Methods for Hermite Polynomials
Author(s) -
Clemente Cesarano
Publication year - 2022
Publication title -
international journal of mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
ISSN - 1998-0140
DOI - 10.46300/9101.2022.16.9
Subject(s) - hermite polynomials , mathematics , orthogonal polynomials , formalism (music) , wilson polynomials , algebra over a field , classical orthogonal polynomials , pure mathematics , discrete orthogonal polynomials , art , musical , visual arts
We exploit methods of operational nature to derive a set of new identities involving families of polynomials associated with operators providing different realizations of the Weyl group. The identities, we will deal with, extend the Nielsen formulae, valid for ordinary Hermite to families of Hermite-like polynomials. It will also be shown that the underlying formalism yields the possibility of obtaining further identities relevant to multi-variable and multi-index polynomials.