The asymptotic behavior of systems of polynomials defined by linear second order recurrence relations of the form; where , is studied. As an application of the results, the domains of convergence of polynomial series of the form 1 with lim sup are determined, and the well known Abel's lemma for power series is extended to such series under appropriate assumptions. The latter problem had been previously addressed by professor Miguel Dumett in  from a different point of view.
Palabras claves. Linear second order recurrence relations, independen solutions, asymptotic behavior of solutions, bounded and uniformly bounded variation, Chebyshev, Legendre, Gegenbauer and Jacobi polynomials, Abel-Picard convergence.