e-mail: pacomarc@ing.uc3m.es

**Orthogonality of linear combinations of two sequences
of orthogonal polynomials**

**Abstract**

We find necessary and sufficient conditions for some linear combinations
of two sequences of monic polynomials orthogonal with respect to linear
functionals *u*, *v*, respectively, be again orthogonal. The
situation of convex linear combinations is analyzed more carefully. Some
kind of perturbations in the parameters of the three-term recurrence relation
appear in a natural way.

Finally, we compare our results with a previous one ([1]) for orthogonal polynomials on the unit circle.

This is a joint work with K. H. Kwon and J. H. Lee (KAIST, Taejon, South Korea).

**Reference**

1. A. Cachafeiro and F. Marcellan, *On convex linear combinations
of sequences of monic polynomials*, Proc. Amer. Math. Soc. **126**
(1998), 2323-2331.