A generalization of the symmetric classical polynomials: Hermite and Gegenbauer polynomials. Issue 3 (3rd March 2016)

• Record Type: Journal Article
• Authors: Romdhane, Neila Ben; Gaied, Mohamed
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 3(2016)
• Page Start: 227
• Page End: 244
• Publication Date: 2016-03-03
• Subjects: d-symmetric classical d-orthogonal polynomials -- generating functions -- component sets -- inversion formula -- d-dimensional functional vector -- moments; 42C05 -- 33C45; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2015.1114483
• Languages: English
• ISSNs: 1065-2469

Abstract

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.