An operational point of view for the theory of multi-variable/multi-index Hermite polynomials

The use of algebraic tools of operational and umbral nature is exploited to develop a new perspective and to extend the theory of Hermite polynomials, with more than one variable also of complex nature. The techniques we adopt includes multivariable/many index Hermite- Kampè-dè-Fèrièt polynomials of order two and higher. It will be shown that the treatment, foreseen here, simplifies the study of the relevant properties and the associated computational technicalities.