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On the zeros of d-symmetric d-orthogonal polynomials

Authors:	N Ben Romdhane

Institution:	Institut Préparatoire aux Études d'Ingénieur de Monastir, Département de Préparation en Math-Physique, 5019 Monastir, Tunisia

Abstract:	In this paper, we give some properties of the zeros of d-symmetric d-orthogonal polynomials and we localize these zeros on (d+1) rays emanating from the origin. We apply the obtained results to some known polynomials. In particular, we partially solve the conjecture about the zeros of the Humbert polynomials stated by Milovanovi? and Dordevi? G.V. Milovanovi?, G.B. Dordevi?, On some properties of Humbert's polynomials, II, Ser. Math. Inform. 6 (1991) 23-30]. A study of the eigenvalues of a particular banded Hessenberg matrix is done.

Keywords:	Recurrence relation d-Orthogonal polynomials d-Symmetric polynomials d-Orthogonal Chebyshev polynomials Gould-Hopper polynomials q-Analogies of generalized Hermite's polynomials Humbert polynomials Hessenberg matrix
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