Math. Model. Nat. Phenom.
Volume 12, Number 3, 2017Special functions and analysis of PDEs
|Page(s)||44 - 50|
|Published online||31 May 2017|
Operational Methods and New Identities for Hermite Polynomials
Section of Mathematics - International Telematic University Uninettuno Corso Vittorio Emanuele II, 39, 00186 Rome, Italy
* Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 42C05 / 33C45 / 33C47
Key words: orthogonal polynomials / Hermite / Weyl group / monomiality principle / generating functions
© EDP Sciences, 2017
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