From Hermite to Humbert polynomials

G. Dattoli, S. Lorenzutta, C. Cesarano

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Abstract

We use the multivariable Hermite polynomials to derive integral representations of Chebyshev and Gegenbauer polynomials. It is shown that most of the properties of these classes of polynomials can be deduced in a fairly straightforward way from this representation, which proves a unifying framework for a large body of polynomial families, including forms of the Humbert and Bessel type, which are a natural consequence of the point of view developed in this paper.
Original languageEnglish
Pages (from-to)37 - 48
Number of pages12
JournalRendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume35
Publication statusPublished - 2003
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Dattoli, G., Lorenzutta, S., & Cesarano, C. (2003). From Hermite to Humbert polynomials. Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 35, 37 - 48.