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The use of algebraic tools of operational and umbral nature is exploited todevelop a new point of view and to extend the theory of Hermite polynomials,with more than one variable also of complex nature. The techniques we adoptincludes multivariable/many index Hermite- Kampe-de-Feriet polynomials of ordertwo and higher. It will be shown that the treatment, foreseen here, simplifiesthe study of the relevant properties and the associated computationaltechnicalities.

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