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. © 1996 Academic Press, Inc.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Dattoli, G., Lorenzutta, S., Maino, G., Torre, A., & Cesarano, C. (1996). Generalized Hermite polynomials and supergaussian forms. Journal of Mathematical Analysis and Applications, 203(3), 597 - 609. https://doi.org/10.1006/jmaa.1996.0399