IJPAM: Volume 100, No. 1 (2015)

OPERATIONAL IDENTITIES ON GENERALIZED
TWO-VARIABLE CHEBYSHEV POLYNOMIALS

C. Cesarano$^1$, C. Fornaro$^2$
$^{1,2}$Università Telematica Internazionale Uninettuno
Rome, ITALY
c.cesarano@uninettunouniversity.net


Abstract. We use the concepts and the formalism of the generalized, m-order, two-variable Hermite polynomials of type $H_{n}^{(m)}(x,y)$ in order to derive integral representations of a generalized family of Chebyshev polynomials. Most properties of these polynomials sets can be deduced in a fairly straightforward way from this representation, which actually provides a unifying framework for a large body of polynomials families related to the Gould-Hopper polynomials. It is evident the present generalizations, obtained by using the generalized Hermite polynomials and the integral representation technique, have led to families of Chebyshev polynomials directly related the ordinary case and then we can recognize the generalizations presented in this paper as Chebyshev-like polynomials.

Received: December 1, 2014

AMS Subject Classification: 33C45, 33D45

Key Words and Phrases: Chebyshev polynomials, Hermite polynomials, Integral representations

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DOI: 10.12732/ijpam.v100i1.6 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: 100
Issue: 1
Pages: 59 - 74


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