IJPAM: Volume 98, No. 2 (2015)

A NOTE ON A SPECIAL CLASS OF HERMITE POLYNOMIALS

C. Cesarano$^1$, C. Fornaro$^2$, L. Vazquez$^3$
$^{1,2}$Università Telematica Internazionale Uninettuno
Rome, ITALY
$^3$Universidad Complutense de Madrid
Madrid, SPAIN


Abstract. This paper is devoted to the description of a special class of Hermite polynomials of five variables. It can be seen as an extension of the generalized vectorial Hermite polynomials of type $H_{m,n}(x,y)$ and at the same time as a generalization of the Gould-Hopper Hermite polynomials of type $H_n(x,y)$. We use the five-variable Hermite polynomials to derive reformulations of the well known operational relations satisfied from the generalized Hermite polynomials of different types.

Received: October 11, 2014

AMS Subject Classification: 42C05, 33C45, 33C47

Key Words and Phrases: Hermite polynomials, orthogonal polynomials, generating functions

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DOI: 10.12732/ijpam.v98i2.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 2
Pages: 261 - 273


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