Abstract
Douak and Maroni stated the following problem:
P1: For fixed non-negative integer r and positive integer d, find all d-orthogonal polynomial sets {P n } n ≥ 0 which satisfy
They solved it for the particular cases (r, d)=(1, 1) and (r, d)=(1, 2). In this paper, we show that the d-orthogonal Faber polynomials are solution of P1 for generals r and d. We also solve P1 for r=1, 2 and general d with the d-symmetry property as an additional condition. Some properties of the obtained polynomials are singled out.
Acknowledgements
The author thanks Professor Y. Ben Cheikh for many enlightening discussions, and the referee for his/her careful reading of the manuscript and corrections.