It is shown that the polynomials introduced recently by Aldaya, Bisque
rt, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection wi
th a relativistic generalization of the quantum harmonic oscillator ca
n be expressed in terms of Gegenbauer polynomials. This fact is useful
in the investigation of the properties of the corresponding wave func
tion. Some examples are given, in particular, related to the asymptoti
c behavior and to the distribution of zeros of the polynomials for lar
ge quantum numbers.