Generalized Hermite polynomials and supergaussian forms

G. Dattoli, S. Lorenzutta, G. Maino, A. Torre, C. Cesarano

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Abstract

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.
Original languageEnglish
Pages (from-to)597 - 609
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume203
Issue number3
DOIs
Publication statusPublished - 1 Nov 1996
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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