Generalized Hermite Polynomials and Supergaussian Forms

We discuss Hermite polynomials of the Gould]Hopper type, the associated harmonic oscillator-like functions, the differential equations they satisfy, and the relevant creation]annihilation operator algebra. We also introduce many variable Hermite polynomials of the Bell type, analyze their properties, and show that they are a natural tool to develop the theory of super-Gauss]Hermite functions, whose pseudo-orthogonal properties are also discussed