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Generalization of two-variable Chebyshev and Gegenbauer polynomials

Clemente Cesarano

Abstract


We use the concepts and the formalism of the two-variable Hermite polynomials of the Gould-Hopper type in order to derive integral representations of the Chebyshev and Gegenbauer polynomials. Most properties of these polynomial sets can be deduced in a fairly straightforward way from thisrepresentation, which actually provides a unifying framework for a large body of polynomial families related to the Gould-Hopper polynomials.

Keywords


Generalized two-variable Chebyshev and Gegenbauer polynomials, Integral representations

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