Theory of generalized hermite polynomials

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

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Abstract

We introduce multivariable generalized forms of Hermite polynomials and analyze both the Gould-Hopper type polynomials and more general forms, which are analogues of the classical orthogonal polynomials, since they represent a basis in L2(RN) Hilbert space, suitable for series expansion of square summable functions of N variables: Moreover, the role played by these generalized Hermite polynomials in the solution of evolution-type differential equations is investigated: The key-note of the method leading to the multivariable polynomials is the introduction of particular generating functions, following the same criteria underlying the theory of multivariable generalized Bessel functions. © 1994.
Original languageEnglish
Pages (from-to)71 - 83
Number of pages13
JournalComputers and Mathematics with Applications
Volume28
Issue number4
DOIs
Publication statusPublished - 1994
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Dattoli, G., Chiccoli, C., Lorenzutta, S., Maino, G., & Torre, A. (1994). Theory of generalized hermite polynomials. Computers and Mathematics with Applications, 28(4), 71 - 83. https://doi.org/10.1016/0898-1221(94)00128-6