On the zeros of d-symmetric d-orthogonal polynomials

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 Milovanovic and Dordevic [G.V. Milovanovic, G.B. Dordevic, On some properties of Humbert's polynomials, II, Ser. Math. Inform. 6 (1991) 23-301. A study of the eigenvalues of a particular banded Hessenberg matrix is done. (C) 2008 Elsevier Inc. All rights reserved.