OPERATIONAL IDENTITIES ON GENERALIZED TWO-VARIABLE CHEBYSHEV POLYNOMIALS

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.