By starting from the concepts and the related formalism of the Monomiality Principle, we exploit methods of operational nature to describe different families of Laguerre polynomials, ordinary and generalized, and to introduce the Legendre polynomials through a special class of Laguerre polynomials themselves. Many of the identities presented, involving families of different polynomials were derived by using the structure of the operators who satisfy the rules of a Weyl group. In this paper, we first present the Laguerre and Legendre polynomials, and their generalizations, from an operational point of view, we discuss some operational identities and further we derive some interesting relations involving an exotic class of orthogonal polynomials in the description of Legendre polynomials.

Operational Techniques for Laguerre and Legendre Polynomials

CESARANO C;
2015-01-01

Abstract

By starting from the concepts and the related formalism of the Monomiality Principle, we exploit methods of operational nature to describe different families of Laguerre polynomials, ordinary and generalized, and to introduce the Legendre polynomials through a special class of Laguerre polynomials themselves. Many of the identities presented, involving families of different polynomials were derived by using the structure of the operators who satisfy the rules of a Weyl group. In this paper, we first present the Laguerre and Legendre polynomials, and their generalizations, from an operational point of view, we discuss some operational identities and further we derive some interesting relations involving an exotic class of orthogonal polynomials in the description of Legendre polynomials.
2015
Laguerre polynomials
Legendre polynomials
Weyl group
File in questo prodotto:
File Dimensione Formato  
a062019-091.pdf

non disponibili

Dimensione 570.71 kB
Formato Adobe PDF
570.71 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14086/1687
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
social impact