A generalization of the symmetric classical polynomials: Hermite and Gegenbauer polynomials |
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| Authors: | Neila Ben Romdhane Mohamed Gaied |
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| Affiliation: | 1. école Supérieure des Sciences et de Technologie de H. Sousse, Sousse University, Sousse, Tunisianeila.benromdhane@ipeim.rnu.tn;3. Institut?Supérieur d'Informatique et des Techniques de Communication de H. Sousse, Sousse University, Sousse, Tunisia |
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| Abstract: | In this paper, we give new families of polynomials orthogonal with respect to a d-dimensional vector of linear functionals, d being a positive integer number, and generalizing the standard symmetric classical polynomials: Hermite and Gegenbauer. We state the inversion formula which is used to express the corresponding moments by means of integral representations involving the Meijer G-function. Moreover, we determine some characteristic properties for these polynomials: generating functions, explicit representations and component sets. |
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| Keywords: | d-symmetric classical d-orthogonal polynomials generating functions component sets inversion formula d-dimensional functional vector moments |
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