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 Milovanovi´c andDordevi´c [G.V. Milovanovi´c, G.B. Dordevi´c, 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. © 2008 Elsevier Inc. All rights reserved