Multi-variable Gould-Hopper and Laguerre polynomials

Abstract

The monomiality principle was introduced by G. Dattoli, in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials. In this article we show a general technique to extend themonomiality approach tomulti-index polynomials in several variables. Application to the case of Hermite, Laguerre-type and mixed-type (i.e. between Laguerre and Hermite) are derived.

Keywords

• Exponential operators
• Operational calculus
• Monomial principle
• Gould-Hopfer polynomials
• Multi-variable and multi-index Hermite and Laguerre polynomials